10 operasi matriks
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The document discusses three matrix operations - addition, subtraction, and multiplication. Matrix addition and subtraction are done by adding or subtracting corresponding elements. For matrices to be added or subtracted, they must have the same order. Matrix multiplication can be done by multiplying a matrix by a scalar number or by another matrix. For two matrices to be multiplied, the number of columns of the first matrix must equal the number of rows of the second matrix. Examples are provided to illustrate each operation.
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Matrices
The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.
Determinants - Mathematics
The document discusses determinants and their properties. It defines determinants as scalars associated with square matrices. Determinants can be computed for matrices of any size using expansions by cofactors along rows or columns. The key properties of determinants are that they are unchanged by row operations and that the inverse of a non-singular matrix can be computed using the adjugate matrix divided by the determinant. The document provides examples of computing the determinant, adjugate, and inverse of matrices.
Matrix and Determinants
Matrices and their operations were discussed. Key points include:
1) A matrix is a rectangular array of numbers. The order of a m x n matrix refers to its m rows and n columns.
2) Common matrix types include row/column matrices (vectors), square matrices, diagonal matrices, scalar matrices, identity matrices, and zero matrices.
3) Basic matrix operations include addition, subtraction, multiplication by a scalar, transpose, and multiplication. Properties like commutativity, associativity, and distributivity apply.
Matrices y determinants
This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.
Matrices And Determinants
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
Matrices
This document discusses matrices and their properties. It defines what a matrix is and different types of matrices such as line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also covers operations that can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Properties of these operations are provided.
Determinants
The document defines determinants as values that can be computed from the elements of a square matrix. Determinants are used throughout mathematics, including in solving systems of linear equations, change of variables rules for integrals, eigenvalue problems, and expressing volumes of parallelepipeds. The determinant of a matrix product equals the product of the determinants, showing that the determinant is a multiplicative map. A matrix is invertible if and only if its determinant is non-zero.
Matrices and determinants-1
All mathematical truths are relative and conditional. Determinants are numbers associated with square matrices that represent the signed area or volume of geometric objects defined by the matrices. This document defines properties of determinants, such as how they are calculated for different sized matrices, how operations on the rows and columns of a matrix affect its determinant, and properties like determinants of diagonal, symmetric, and skew-symmetric matrices. It also provides examples of using determinants to find equations of lines and the area of triangles.
Recommended
Matrices
The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.
Determinants - Mathematics
The document discusses determinants and their properties. It defines determinants as scalars associated with square matrices. Determinants can be computed for matrices of any size using expansions by cofactors along rows or columns. The key properties of determinants are that they are unchanged by row operations and that the inverse of a non-singular matrix can be computed using the adjugate matrix divided by the determinant. The document provides examples of computing the determinant, adjugate, and inverse of matrices.
Matrix and Determinants
Matrices and their operations were discussed. Key points include:
1) A matrix is a rectangular array of numbers. The order of a m x n matrix refers to its m rows and n columns.
2) Common matrix types include row/column matrices (vectors), square matrices, diagonal matrices, scalar matrices, identity matrices, and zero matrices.
3) Basic matrix operations include addition, subtraction, multiplication by a scalar, transpose, and multiplication. Properties like commutativity, associativity, and distributivity apply.
Matrices y determinants
This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.
Matrices And Determinants
Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]
Matrices
This document discusses matrices and their properties. It defines what a matrix is and different types of matrices such as line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also covers operations that can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Properties of these operations are provided.
Determinants
The document defines determinants as values that can be computed from the elements of a square matrix. Determinants are used throughout mathematics, including in solving systems of linear equations, change of variables rules for integrals, eigenvalue problems, and expressing volumes of parallelepipeds. The determinant of a matrix product equals the product of the determinants, showing that the determinant is a multiplicative map. A matrix is invertible if and only if its determinant is non-zero.
Matrices and determinants-1
All mathematical truths are relative and conditional. Determinants are numbers associated with square matrices that represent the signed area or volume of geometric objects defined by the matrices. This document defines properties of determinants, such as how they are calculated for different sized matrices, how operations on the rows and columns of a matrix affect its determinant, and properties like determinants of diagonal, symmetric, and skew-symmetric matrices. It also provides examples of using determinants to find equations of lines and the area of triangles.
Matrices & determinants
The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.
Matrices and determinants
This document discusses matrix algebra concepts such as determinants, inverses, eigenvalues, and rank. It provides the following key points:
- The determinant of a square matrix is a number that characterizes properties like singularity. It is defined as the sum of products of the matrix elements.
- Cramer's rule provides a formula for solving systems of linear equations using determinants, but it is only practical for small matrices up to 3x3 or 4x4 due to computational complexity.
- A matrix is singular if its determinant is zero, meaning its rows and columns are linearly dependent. The rank of a matrix is the size of the largest non-singular sub-matrix. A full rank matrix has
Ppt on matrices and Determinants
Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.
Report in determinants
The determinant of a square matrix provides important information about the associated linear transformation and solutions to systems of linear equations. It can be computed from the entries of the matrix using specific arithmetic expressions. For a 2x2 matrix, the determinant is defined as the product of diagonal entries minus the product of off-diagonal entries. The absolute value of the determinant gives the scale factor by which area or volume is multiplied under the linear transformation, while the sign indicates if orientation is preserved. Determinants occur throughout mathematics and are used in calculus, linear algebra, and as a compact notation for expressions.
yaron_eurika_
1) The document presents a method called the "spiral concatenation unfolding operator" for expressing trigonometric and hyperbolic functions as rational expressions consisting of powers of the original function.
2) The method involves: a) extracting the function into real and imaginary parts using binomial coefficients, b) tagging each term as numerator or denominator, and c) rearranging the terms into a "spiral concatenation" rational expression.
3) Examples are provided to demonstrate the method for expressing tg(n), ctg(n), tgh(n), and ctgh(n) as rational functions of the respective base function.
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- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.
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The document describes the Gauss-Seidel method for solving a system of linear equations. The method works by decomposing the coefficient matrix A into lower and upper triangular matrices L* and U. It then iteratively solves the system Ax=b by using forward substitution to sequentially compute updated values for each element of x, where the computation of x_i(k+1) uses the most recent values from x(k) except for x_i(k). This process is repeated until subsequent iterations produce changes in x below a specified tolerance level.
Ma3bfet par 10.5 31 julie 2014
1. Homework Task 3 on systems of equations and inequalities is due on August 6. Students should check all memos on the online learning platform.
2. The document discusses finding inverses of matrices and solving matrix equations. It provides examples of finding the inverse of 2x2 and 3x3 matrices using elementary row operations to transform the matrices into an identity matrix.
3. Solving a system of equations using a matrix inverse involves writing the system as a matrix equation AX=B, then multiplying both sides by the inverse of the coefficient matrix A to isolate the solution vector X.
Ppt on matrices
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
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This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.
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This document discusses laws of logarithms and inverse functions. It provides examples of solving logarithmic equations using the laws of logarithms, such as loga4 + loga6 = loga(x + 4). It also defines inverse functions as functions where the composition of the functions results in the original input. An example shows that f(x) = 1x/3 - 3 and g(x) = 3x + 9 are inverse functions by computing their compositions.
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This document defines common matrix notation and operations such as matrix addition, scalar multiplication, and matrix multiplication. It also covers properties of these operations, as well as the transpose and powers of a matrix. Key concepts include representing a matrix as a collection of columns representing vectors, defining entries and dimensions of a matrix, and rules for matrix algebra like the associative and distributive properties.
Algebraic Properties of Matrix Operations
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thú vị lắm nhé các bạ nào muốn học toán bằng tiếng anh thì hãy vào làm thử nhé, những câu hỏi rất đơn giản nhưng cần phải tư duy cũng mất hơi nhiều thời gian. tôi mong là các bạn sẽ thích tài liệu này của tôi. cảm ơn các bạn đã xem. nếu ai chưa có câu trả lời thì hãy nhắn tin cho tôi nhé
Determinants
The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.
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Logarithmic functions are the inverse of exponential functions. They allow mathematicians to write exponential expressions like 2x = 6 in logarithmic form as log2 6 = x. The graph of a logarithmic function y = logb(x - h) + k will increase if b > 1 and decrease if 0 < b < 1. It will have a vertical asymptote at x = h. Logarithmic functions have the opposite domain and range from their inverse exponential functions.
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The document provides instructions for sketching the graphs of various absolute value functions. It includes sketching the graphs of y=|x|, y=|2x+4|+1, and graphing y=-2|1/4x-1|-3 on a graphing calculator. It also asks how to type the equation -3y+9=6|x-12| into the graphing calculator.
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Matriks adalah susunan bilangan dakam bentuk baris dan kolom, biasanya dilambangkan dalam huruf capital.
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This document discusses matrices and their properties. It begins by defining what a matrix is - a collection of numbers arranged in rows and columns. It notes that matrices were first introduced in 1859 and are now used widely in fields like quantum mechanics. The document then covers various matrix topics in detail over multiple sections, including notation and order, basic operations like addition/subtraction and multiplication, determinants, inverses, similarities and equations. It provides examples for each topic to illustrate the concepts and rules regarding matrices.
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Matrices & determinants
The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.
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This document discusses matrix algebra concepts such as determinants, inverses, eigenvalues, and rank. It provides the following key points:
- The determinant of a square matrix is a number that characterizes properties like singularity. It is defined as the sum of products of the matrix elements.
- Cramer's rule provides a formula for solving systems of linear equations using determinants, but it is only practical for small matrices up to 3x3 or 4x4 due to computational complexity.
- A matrix is singular if its determinant is zero, meaning its rows and columns are linearly dependent. The rank of a matrix is the size of the largest non-singular sub-matrix. A full rank matrix has
Ppt on matrices and Determinants
Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.
Report in determinants
The determinant of a square matrix provides important information about the associated linear transformation and solutions to systems of linear equations. It can be computed from the entries of the matrix using specific arithmetic expressions. For a 2x2 matrix, the determinant is defined as the product of diagonal entries minus the product of off-diagonal entries. The absolute value of the determinant gives the scale factor by which area or volume is multiplied under the linear transformation, while the sign indicates if orientation is preserved. Determinants occur throughout mathematics and are used in calculus, linear algebra, and as a compact notation for expressions.
yaron_eurika_
1) The document presents a method called the "spiral concatenation unfolding operator" for expressing trigonometric and hyperbolic functions as rational expressions consisting of powers of the original function.
2) The method involves: a) extracting the function into real and imaginary parts using binomial coefficients, b) tagging each term as numerator or denominator, and c) rearranging the terms into a "spiral concatenation" rational expression.
3) Examples are provided to demonstrate the method for expressing tg(n), ctg(n), tgh(n), and ctgh(n) as rational functions of the respective base function.
Matrices - multiplication of matrices
- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.
Gaussseidel
The document describes the Gauss-Seidel method for solving a system of linear equations. The method works by decomposing the coefficient matrix A into lower and upper triangular matrices L* and U. It then iteratively solves the system Ax=b by using forward substitution to sequentially compute updated values for each element of x, where the computation of x_i(k+1) uses the most recent values from x(k) except for x_i(k). This process is repeated until subsequent iterations produce changes in x below a specified tolerance level.
Ma3bfet par 10.5 31 julie 2014
1. Homework Task 3 on systems of equations and inequalities is due on August 6. Students should check all memos on the online learning platform.
2. The document discusses finding inverses of matrices and solving matrix equations. It provides examples of finding the inverse of 2x2 and 3x3 matrices using elementary row operations to transform the matrices into an identity matrix.
3. Solving a system of equations using a matrix inverse involves writing the system as a matrix equation AX=B, then multiplying both sides by the inverse of the coefficient matrix A to isolate the solution vector X.
Ppt on matrices
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
Calculus
This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.
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This document discusses laws of logarithms and inverse functions. It provides examples of solving logarithmic equations using the laws of logarithms, such as loga4 + loga6 = loga(x + 4). It also defines inverse functions as functions where the composition of the functions results in the original input. An example shows that f(x) = 1x/3 - 3 and g(x) = 3x + 9 are inverse functions by computing their compositions.
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This document defines common matrix notation and operations such as matrix addition, scalar multiplication, and matrix multiplication. It also covers properties of these operations, as well as the transpose and powers of a matrix. Key concepts include representing a matrix as a collection of columns representing vectors, defining entries and dimensions of a matrix, and rules for matrix algebra like the associative and distributive properties.
Algebraic Properties of Matrix Operations
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The m x n matrix with all entries of zero is denoted by 푶_풎풏 , for a matrix A of size m x n, we have:
Diagonalization of Matrices
The document discusses diagonalization of matrices. Diagonalization involves finding an invertible matrix P such that P-1AP is a diagonal matrix. The procedure for diagonalizing a matrix A includes: (1) finding the eigenvalues of A, (2) finding linearly independent eigenvectors corresponding to the eigenvalues, (3) forming the matrix P with the eigenvectors as columns, and (4) showing that P-1AP is a diagonal matrix with the eigenvalues along the diagonal. An example demonstrates finding the eigenvectors of a 2x2 matrix A and constructing the matrix P to diagonalize A.
Week 1
thú vị lắm nhé các bạ nào muốn học toán bằng tiếng anh thì hãy vào làm thử nhé, những câu hỏi rất đơn giản nhưng cần phải tư duy cũng mất hơi nhiều thời gian. tôi mong là các bạn sẽ thích tài liệu này của tôi. cảm ơn các bạn đã xem. nếu ai chưa có câu trả lời thì hãy nhắn tin cho tôi nhé
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The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.
A28-4 log fxns
Logarithmic functions are the inverse of exponential functions. They allow mathematicians to write exponential expressions like 2x = 6 in logarithmic form as log2 6 = x. The graph of a logarithmic function y = logb(x - h) + k will increase if b > 1 and decrease if 0 < b < 1. It will have a vertical asymptote at x = h. Logarithmic functions have the opposite domain and range from their inverse exponential functions.
Integration
This document discusses integration in mathematics. It defines integration as the process opposite to differentiation, where integration finds the direct relationship between two variables given their rate of change. Several techniques for integration are described, including integration by parts and substitution. The document outlines the history of integration and its applications in fields like engineering, business, and its use in estimating important values.
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A matrix is a rectangular array of numbers arranged in rows and columns. There are several types of matrices including square, rectangular, diagonal, identity, and triangular matrices. Operations that can be performed on matrices include addition, subtraction, multiplication by a scalar, and determining the transpose, determinant, and inverse of a matrix. A C program is shown that uses nested for loops to input and output the elements of a matrix.
Alg2 Notes Unit 1 Day 5
The document provides instructions for sketching the graphs of various absolute value functions. It includes sketching the graphs of y=|x|, y=|2x+4|+1, and graphing y=-2|1/4x-1|-3 on a graphing calculator. It also asks how to type the equation -3y+9=6|x-12| into the graphing calculator.
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This document provides an overview of matrices including:
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1. The document discusses matrices and various matrix operations.
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K-Notes are concise study materials intended for quick revision near the end of preparation for exams like GATE. Each K-Note covers the concepts from a subject in 40 pages or less. They are useful for final preparation and travel. Students should use K-Notes in the last 2 months before the exam, practicing questions after reviewing each note. The document then provides a summary of key concepts in linear algebra and matrices, including matrix properties, operations, inverses, and systems of linear equations.
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MATRICES maths project.pptxsgdhdghdgf gr to f HR f
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ALLIED MATHEMATICS -I UNIT III MATRICES.ppt
Matrices can be represented as arrays of numbers arranged in rows and columns. A matrix is defined by its dimensions (number of rows and columns). There are several types of matrices including square, rectangular, diagonal, identity, null, triangular, and scalar matrices. Operations on matrices include addition, subtraction, and multiplication. For matrices to be added or subtracted, they must be the same size. Matrices can be multiplied by a scalar value. Matrix multiplication results in another matrix, and the number of columns of the first matrix must equal the number of rows of the second matrix.
chap01987654etghujh76687976jgtfhhhgve.ppt
This document provides an overview of matrices and determinants. It begins by defining a matrix as a rectangular array of numbers enclosed in brackets. It discusses types of matrices such as square matrices and zero matrices. It covers basic matrix operations like addition, subtraction, and scalar multiplication. It also explains matrix multiplication and some of its key properties. Special matrices are introduced, including identity, inverse, transpose, symmetric, and orthogonal matrices. The document uses examples throughout to illustrate matrix concepts and operations.
Matrices
Some types of matrices, Eigen value , Eigen vector, Cayley- Hamilton Theorem & applications, Properties of Eigen values, Orthogonal matrix , Pairwise orthogonal, orthogonal transformation of symmetric matrix, denationalization of a matrix by orthogonal transformation (or) orthogonal deduction, Quadratic form and Canonical form , conversion from Quadratic to Canonical form, Order, Index Signature, Nature of canonical form.
Basic concepts. Systems of equations
This document defines and provides examples of different types of matrices:
- Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix.
- The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints.
- A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal.
- The transpose of a matrix exchanges the rows and columns of the original matrix.
- The inverse of an invertible square matrix results in the identity matrix when multiplied by the original.
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MATRICES maths project.pptxsgdhdghdgf gr to f HR f
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10 operasi matriks
- 1. OPERASI MATRIKS 1. Penjumlahan matriks Misalkan terdapat dua buah matriks, yaitu matriks A dan matriks B. Jika matriks C adalah matriks penjumlahan dari A dengan B, maka matriks C dapat diperoleh dengan menjumlahkan setiap elemen pada matriks A yang seletak dengan setiap elemen pada matriks B. Oleh karena itu, syarat agar dua atau lebih matriks dapat dijumlahkan adalah harus memiliki ordo yang sama. Contoh: A + B = ( 1 + 4 2 + 1 4 + (−4) 6 + 5 ) = ( 5 3 0 11 ) 2. Pengurangan matriks Misalkan terdapat dua buah matriks, yaitu matriks A dan matriks B. Jika matriks C adalah matriks pengurangan dari A dengan B, maka matriks C dapat diperoleh dengan mengurangkan setiap elemen pada matriks A yang seletak dengan setiap elemen pada matriks B. Contoh: A – B = ( −7 − 1 5 − 1 4 − (−4) 8 − 9 ) = ( −8 −4 8 −1 ) 3. Perkalian Matriks A. Perkalian matriks dengan bilangan real (skalar) Misalkan terdapat matriks A berordo m × n dan suatu bilangan real (skalar), yaitu k. Perkalian antara matriks A dengan skalar k dapat ditulis dengan kA yang diperoleh dengan mengalikan setiap elemen matriks A dengan skalar k. K( 𝑎 𝑐 𝑏 𝑑 ) = ( 𝑘. 𝑎 𝑘. 𝑐 𝑘. 𝑏 𝑘. 𝑑 ) Contoh : −2( 3 4 −1 0 ) = ( −2 𝑥 3 −2 𝑥 4 −2 𝑥 − 1 −2 𝑥 0 ) = ( −6 −8 2 0 )
- 2. B. Perkalian matriks dengan matriks Misalkan terdapat dua buah matriks, yaitu matriks A dengan ordo m × p dan matriks B dengan ordo p × n. Perkalian matriks A dengan matriks B dapat ditulis dengan A × B yang diperoleh dari penjumlahan hasil kali elemen-elemen yang bersesuaian pada baris ke-i matriks A dengan kolom ke-j matriks B. Syarat agar dua buah matriks dapat dikalikan adalah matriks pertama harus memiliki jumlah kolom yang sama dengan jumlah baris pada matriks kedua. ( 𝑎 𝑐 𝑏 𝑑 )( 𝑒 𝑔 𝑓 ℎ) = ( 𝑎. 𝑒 + 𝑐. 𝑓 𝑎. 𝑔 + 𝑐. ℎ 𝑏. 𝑒 + 𝑑. 𝑓 𝑏. 𝑔 + 𝑑. ℎ ) Contoh: A X B = ( 6 𝑥 1+ 3 𝑥 2 4 𝑥 1+ 8 𝑥 2 ) = ( 6 + 6 4 + 16 ) = ( 12 20 )