Identity matrix
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An identity matrix is a square matrix with ones along its main diagonal and zeros elsewhere. When a matrix is multiplied by its corresponding identity matrix, the original matrix is returned. The identity matrix for an n×n matrix is denoted In×n. Some key properties of identity matrices are that AI = IA = A for any square matrix A of the same dimensions.
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1.
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If find -2A.
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- Determinants and how to calculate the determinant of 2x2 and 3x3 matrices.
- The inverse of matrices and how to calculate the inverse of 2x2 and 3x3 matrices.
- How matrices can be used to represent and solve business problems involving quantities such as production levels.
4.5 Multiplication Of Two Matrices
The document discusses matrix multiplication. It defines that two matrices can be multiplied if the number of columns of the first matrix is equal to the number of rows of the second matrix. The product matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. Examples are provided to demonstrate how to determine if matrix multiplication is possible and how to calculate the product of two matrices.
4.5 Multiplication Of Two Matrices
The document discusses matrix multiplication. It defines that two matrices can be multiplied if the number of columns of the first matrix is equal to the number of rows of the second matrix. The product matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. Examples are provided to demonstrate how to determine if matrix multiplication is possible and how to calculate the product of two matrices.
Mathematics
The document discusses matrix multiplication. It defines that two matrices can be multiplied if the number of columns of the first matrix is equal to the number of rows of the second matrix. The product matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. Examples are provided to demonstrate how to determine if matrix multiplication is possible and how to calculate the product of two matrices.
Mathematics
The document discusses matrix multiplication. It defines that for two matrices to be multiplied, the number of columns of the first matrix must equal the number of rows of the second matrix. The product matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. Examples are provided to demonstrate determining if matrices can be multiplied and calculating the actual product.
LecturePresentation.pptx
The document describes the substitution method for solving systems of linear equations. It provides examples of using the substitution method to solve systems of two equations with two unknowns. The steps are: (1) solve one equation for one variable, (2) substitute this expression into the other equation and solve, (3) substitute the solution back to find the other variable, (4) write the solution as an ordered pair. Video clips demonstrate the method and examples provide the full working of the substitution method to find the point of intersection for systems of equations. Practice problems are given for readers to try applying the substitution method on their own.
Simultaneous equations
This document provides instructions for solving simultaneous equations using non-graphical methods. It demonstrates the step-by-step process of numbering the equations, eliminating variables, solving for the values of each variable, and checking the solutions in multiple examples.
Determinants.ppt
This document provides an introduction to matrices and determinants. Some key points:
- Matrices are arrays of numbers arranged in rows and columns. Determinants are single numbers associated with square matrices.
- Methods are presented for calculating the determinants of 2x2 and 3x3 matrices, including the diagonal and cofactor methods.
- The determinant of a matrix is used to find the inverse of a matrix and in calculating the area of triangles.
- Matrix operations like multiplication and solving systems of equations can be represented using matrix notation. The inverse of a matrix allows solving systems of equations written in matrix form.
Class xii practice questions
The document provides properties of determinants and examples of their applications. It also gives tips for solving problems based on properties of determinants. Finally, it lists 20 assignment questions related to matrices and determinants, covering topics like solving systems of equations using matrices, finding the inverse of a matrix, and applying properties of determinants.
Lesson 3 finding x and y intercepts shared
The document discusses finding the x-intercepts and y-intercepts of graphs and equations. It defines intercepts as the points where the line crosses the x-axis or y-axis. It then provides examples of finding the intercepts by setting y=0 to find the x-intercept or setting x=0 to find the y-intercept and solving the resulting equation. The document demonstrates this process for multiple equations and graphs. It also introduces the "cover up method" of solving multi-variable equations by covering terms with the same variable to isolate that variable.
Introduction of matrices
The order of the given matrix is 2×3. So the maximum no. of elements is 2×3 = 6.
The correct option is B.
The element a32 belongs to 3rd row and 2nd column.
The correct option is B.
3. A matrix whose each diagonal element is unity and all other elements are zero is called
A) Identity matrix B) Unit matrix C) Scalar matrix D) Diagonal matrix
4. A matrix whose each row sums to unity is called
A) Row matrix B) Column matrix C) Unit matrix D) Stochastic matrix
5. The sum of all the elements on the principal diagonal of a square
Final exam review #2
The document provides a review for an Algebra II final exam covering topics such as linear equations and inequalities, rational expressions, complex numbers, matrices, and polynomial functions. The review contains 50 practice problems across 7 sections testing different algebra concepts and skills needed to solve various types of problems.
Zeros of a polynomial function
The document discusses polynomial functions and their roots. It begins by defining that the roots of a polynomial function are the values of x that make the function equal to 0. It then provides examples of finding the roots of linear and quadratic equations. Next, it introduces the Rational Root Theorem, which states that possible rational roots must be factors of the constant term and leading coefficient. Examples are given to demonstrate applying the theorem. The document concludes by using synthetic division to find all three roots of a cubic polynomial given one known root.
Matrices and determinants_01
This document provides definitions and properties of matrices and determinants. Some key points include:
- A matrix is a rectangular array of numbers or expressions. The order of a matrix refers to its number of rows and columns.
- Special types of matrices include square, diagonal, identity, and zero matrices. Transpose of a matrix is obtained by interchanging rows and columns.
- Determinants can be calculated for square matrices and have various properties. The adjoint and inverse of a matrix are also defined.
- Systems of linear equations can be solved using matrices by computing the inverse or using properties of determinants.
Similar to Identity matrix (20)
1. Which of the following is the correct matrix representation .docx
1. Which of the following is the correct matrix representation .docx
Identity matrix
- 1. 4.6IDENTITY MATRIX LOH HUI YI CHANG WAN LING LEE CHAI EN KAM SIEW HUEY
- 2. Definition An identity matrix, I, is a matrix which when multiplying it to another matrix, such as A, the product is the matrix A itself. IA = A and AI = A AI = IA = A
- 3. Identity Matrix is also called as Unit Matrix or Elementary Matrix. Identity Matrix is denoted with the letter “In×n”, where n×n represents the order of the matrix. One of the important properties of identity matrix is: A×In×n = A, where A is any square matrix of order n×n.
- 4. A matrix with the same number of rows and columns is called a squarematrix. 3x3
- 5. An identity matrix, I, is a square matrix and the elements are 0 and 1 only. The elements in the main diagonal are 1 while the others are 0. 1 0 0 0 1 0 0 0 1 I = 3 x 3
- 6. EXAMPLE 1 1 2 1 1 3 7 3 4 1 1 3 7 so 1 1 1 1 is not an identity matrix
- 7. EXAMPLE 2 1 2 1 0 1 2 3 4 0 1 3 4 so 1 0 0 1 is the identity for 2x2 matrices
- 8. EXERCISES 1 1 2 1 0 -2 1 0 1 2 1 0 1 2 0 1 -2 1 2 -2 1 2 -2 1
- 10. Solution:Step 1: M = -4 -3 (Given) -6 5Step 2: As M is square matrix of order 2×2, the identity matrix I is also of same order 2×2. (Rule for Matrix Multiplication)Step 3: Then M×I = -4 -3 1 0 -6 5 0 1 = (-4x1)+(-3x0) (-4x0)+(-3x1) (-6x1)+(5x0) (-6x0)+(5x1) (Matrix Multiplication) ×
- 11. Step 4: = -4 -3 -6 5 (Simplifying) Step 5: Hence M×I = M = -4 -3 -6 5 #