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This document provides instructions for performing various operations on matrices using Microsoft Excel. It begins by stating the intended audience and objectives, which are to learn how to add and subtract matrices, multiply a matrix by a scalar, multiply two matrices, and find the determinant and inverse of a matrix using Excel. The document then provides definitions and examples of matrices. It proceeds to explain how to add and subtract matrices by adding the corresponding elements. It also explains how to multiply a matrix by a scalar and multiply two matrices according to the standard rules. The document demonstrates how to use Excel formulas like MMULT, MDETERM, and MINVERSE to calculate the product, determinant, and inverse of matrices. It concludes by providing some additional resources on the topic
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This document provides an introduction to MATLAB. It begins with an overview of the MATLAB environment and display windows. It then discusses getting help in MATLAB, variables, vectors, matrices, linear algebra, plotting, built-in functions, selection programming using if/else statements, M-files, user-defined functions, and specific topics. Key points covered include the MATLAB interface, basic programming constructs like variables and arrays, and tools for computation, visualization, and programming in MATLAB.
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The document discusses exponents and order of operations. It defines exponents as indicating how many times the base is used as a factor. It provides examples of evaluating exponential expressions by writing repeated factors with exponents. Rules for exponents include: any number to the power of 0 equals 1; any number to the power of 1 equals the number; and multiplying exponents when the bases are the same. The order of operations is explained as: exponents, multiplication/division from left to right, and addition/subtraction from left to right. Grouping symbols like parentheses and fraction bars dictate that operations within are completed first. Several examples demonstrate applying these rules to simplify expressions.
Matrix
This document discusses basic matrix operations including addition, subtraction, and multiplication of matrices by scalars. It defines a matrix as a rectangular arrangement of numbers in rows and columns with entries as the individual numbers. It explains that to add or subtract matrices they must have the same order (number of rows and columns) and the corresponding entries are added or subtracted. It also describes multiplying a matrix by a scalar by multiplying each entry in the matrix by the scalar number.
11th MATRICES PPT.pptx
The document discusses matrices and their operations. It defines a matrix as a rectangular array of numbers and provides examples. It describes how to add, subtract, and multiply matrices by scalars. Matrix multiplication follows certain rules regarding the number of rows and columns. The determinant of a matrix is a single number associated with square matrices. For 2x2 matrices, the determinant is calculated as the product of diagonals subtracted by the product of off-diagonals. Larger matrices use cofactor expansion. Applications include calculating the area of a triangle using a determinant of a 3x1 matrix of vertex coordinates.
Matlab Tutorial
This document provides information on generating and manipulating matrices in MATLAB. It discusses how to explicitly enter small matrices by separating elements with blanks/commas and rows with semicolons. Large matrices can be entered over multiple lines using the return button. Individual elements can be accessed and altered using indices in parentheses. Columns and rows can be appended to matrices using various commands. A colon is used to extract submatrices. Logical operators compare matrices and return 1s and 0s. Functions like diag(), fliplr(), flipud() and rot90() manipulate matrices. Random matrices can be generated using commands like rand() and ones(). Vectors subtracted from matrices using broadcasting. Example problems demonstrate generating matrices from vectors and manipulating the matrices.
Matrix basic operations
This document discusses basic matrix operations including:
- Defining a matrix as a rectangular arrangement of numbers in rows and columns with an order specified by the number of rows and columns.
- Adding and subtracting matrices requires they have the same order, done by adding or subtracting corresponding entries.
- Multiplying a matrix by a scalar involves multiplying each entry in the matrix by the scalar value.
- Matrix multiplication is not commutative and can only be done if the number of columns in the first matrix equals the number of rows in the second, with the result being the multiplication of corresponding entries summed up.
Matrix basic operations
This document discusses basic matrix operations including:
- Defining a matrix as a rectangular arrangement of numbers in rows and columns with an order specified by the number of rows and columns.
- Adding and subtracting matrices requires they have the same order and involves adding or subtracting corresponding entries.
- Multiplying a matrix by a scalar involves multiplying each entry in the matrix by the scalar value.
- Matrix multiplication is not commutative and can only be done if the number of columns in the first matrix equals the number of rows in the second matrix. It involves multiplying entries and summing the products based on their positions.
Introduction to MATLAB
MatLab is a matrix-based program used for numeric computation and visualization. It contains functions for creating matrices and performing operations on them like addition, subtraction, multiplication, etc. It also allows plotting of functions and special matrices like magic squares, identity matrices, and Toeplitz matrices. Polynomial operations can also be performed such as addition, multiplication, differentiation and evaluation.
Matrix basic operations
This document discusses various matrix operations including addition, subtraction, multiplication by a scalar, and matrix multiplication. It defines a matrix as a rectangular arrangement of numbers in rows and columns with an order specified by the number of rows and columns. It explains that to add or subtract matrices they must have the same order, and performing those operations involves adding or subtracting the corresponding entries. It also explains that multiplying a matrix by a scalar involves multiplying each entry of the matrix by the scalar. Matrix multiplication is defined as taking the numbers in each row of the first matrix and multiplying them by the corresponding numbers in the columns of the second matrix, with the result being that the number of columns of the first matrix must equal the number of rows of the
Matrix basic operations
This document discusses various matrix operations including addition, subtraction, multiplication by a scalar, and matrix multiplication. It defines a matrix as a rectangular arrangement of numbers in rows and columns with an order specified by the number of rows and columns. It explains that to add or subtract matrices they must have the same order, and performing those operations involves adding or subtracting the corresponding entries. It also explains that multiplying a matrix by a scalar involves multiplying each entry of the matrix by the scalar. Matrix multiplication is defined as taking the numbers in each row of the first matrix and multiplying them by the corresponding numbers in the columns of the second matrix, with the result being that the number of columns of the first matrix must equal the number of rows of the
bobok
This document provides an overview of MATLAB, including:
- MATLAB is a software package for numerical computation, originally designed for linear algebra problems using matrices. It has since expanded to include other scientific computations.
- MATLAB treats all variables as matrices and supports various matrix operations like addition, multiplication, element-wise operations, and matrix manipulation functions.
- MATLAB allows plotting of 2D and 3D graphics, importing/exporting of data from files and Excel, and includes flow control statements like if/else, for loops, and while loops to structure code execution.
- Efficient MATLAB programming involves using built-in functions instead of custom functions, preallocating arrays, and avoiding nested loops where possible through matrix operations.
Lesson 1 matrix
This document provides an introduction to basic matrix operations including addition, subtraction, scalar multiplication, and matrix multiplication. It defines matrices and how to perform basic arithmetic on matrices. It also introduces the concept of matrix equations and using matrix multiplication to solve systems of linear equations. Key points covered include:
- How to add and subtract matrices by adding or subtracting the corresponding entries
- Scalar multiplication involves multiplying each entry of a matrix by a scalar number
- Matrix multiplication involves multiplying rows of one matrix with columns of another, with the constraint that the number of columns of the first matrix must equal the number of rows of the second matrix.
- Matrix multiplication is not commutative in general.
Matlab level 1.pptx
Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems.
Similar to Final project (20)
Final project
- 2. Intended AudIence Elective Mathematics Senior High School Four (4)
- 3. By the end of the lesson you will be able to use Microsoft excel to: Add and subtract matrices Multiply a matrix by a scalar Multiply two matrices Find determinant and inverse of a matrix
- 4. A matrix (plural-matrices) is a set of numbers arranged in rows and columns enclosed in round or square brackets. The order of a matrix gives the number of rows followed by the number of columns in a matrix.
- 5. −− − 67237 89511 36402 [ ]0759 − − − 3410 200 318 − 20 11 − 6 0 7 9 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a column matrix) (or square matrix) (Also called a row matrix) ORdeR OF MAtRIceS
- 6. ROW COLUMN in excel we enter entries in a cell
- 7. You can only add matrices of the same order. Eg 3 x 3, 2 x 2 or 4 x 4 To add, you simply add the corresponding elements in each matrix. This is can be done algebraically as shown below:
- 8. To add two matrices, they must have the same order. To add, you simply add corresponding entries. − − + − − 34 03 12 70 43 35 −++ ++− +−−+ = )3(740 0433 13)2(5 B − = 44 40 23 Addition and Subtraction of Matrix A
- 9. 1. Enter the data of each matrix. 2. Highlight another section of the worksheet (near the given matrices) that has the same dimensions as the answer matrix. Let's say that we wish to find: [A] + [B] Since we are adding two 3 x 3 matrices, the sum matrix will also be 3 x 3.
- 10. 3. Type: = (A2:C4)+(E2:G4) (This will appear in the formula bar.) 4. Since this answer will result in an array (matrix), you will need to: CTRL+SHIFT+ENTER (NOTE: Braces will surround the formula.) This is shown below;
- 11. The formula
- 12. Enter the data of each matrix. Highlight another section of the worksheet (near the given matrices) that has the same dimensions as the answer matrix. Let's say that we wish to find: [A] – [B] Since we are subtracting two 3 x 3 matrices, the difference matrix will also be 3 x 3.
- 13. Type: =(A2:C4)–(E2:G4) (This will appear in the formula bar Since this answer will result in an array (matrix), you will need to: CTRL+SHIFT+ENTER .). This is shown in the next slide shown in the next slide
- 14. How to multiply a matrix by a scalar (real number): 1. Enter the elements of the given matrix. 2. Highlight another section of the worksheet (near the given matrix) that has the same dimensions as the given matrix. Let's say that we wish to multiply the given matrix (4 x 3) by a scalar of three (3).
- 15. Since we are multiplying a 4 x 3 matrix by the scalar, our result will also be a 4 x 3 matrix. 3. Type: = 3*(A2:C5) (This will appear in the formula bar.) 4. Since this answer will result in an array (matrix), you will need to: CTRL+SHIFT+ENTER
- 16. It is possible to work out the product of two matrices according to the following rules: • the number of columns in the first matrix must be equal to the number of rows in the second matrix. • the order of the product of the matrices is the number of rows in the first matrix multiplied by the number of columns in the second. • when multiplying, multiply the elements of a row of the first matrix by the elements in a column of the second matrix and add the products. Column = 3 Row = 3 NB: Answer = 3 x 2
- 17. •Enter the data to be multiplied • Highlight another section of the worksheet (near the given matrices) that has the same dimensions as the answer matrix. Let's say that we wish to find the product of matrix A (3 x 3) and matrix B (3 x 4). Recall that the number of columns of the first matrix must be equal to the number of rows of the second matrix to produce a product matrix. Therefore, we must find the product of [A] x [B] – which will be a 3 x 4 matrix. How to multiply two matrices:
- 18. Type: = MMULT(A2:C4,E2:H4) (This will appear in the formula bar.) Then press ctrl + shift + enter The result is shown below
- 19. bcadA dc ba AIf −= = , The example below shows how to find the determinant of matrices. NB: Only square matrices have determinants. In other words we can find the determinant for only square matrices. Determinant of a square matrix
- 20. Enter the given matrix Highlight a cell of the worksheet where you wish your answer to appear Type =MDETERM(A2:C4)
- 21. Press the enter key The result is shown below
- 22. 1. Enter the square matrix that is to be inverted. 2. Highlight another section of the worksheet (near the given matrix) that has the same dimensions as the given square matrix. Since we were given a 3 x 3 matrix, its inverse will also be a 3 x 3 matrix. 3. Type: = MINVERSE(A2:C4) (This will appear in the formula bar.)
- 23. 4. Since this answer will result in an array (matrix), you will need to: Press CTRL+SHIFT+ENTER This shown below
- 26. www.google.com/solving matrices with excel. Tutorial on using excel to solve matrices by Mr. Ampiah, (University of Education, Winneba) Using Microsoft Excel 2007 to Perform Matrix Operations by Donna M. Wacha, (Monmouth University)