To verify whether a matrix B is the inverse of the given matrix A, we need to check whether the product of the two matrices is equal to the identity matrix I. You can use a spreadsheet to find the product of two matrices. A= 1 2 3 2 5 3 1 0 8 B= -40 16 9 13 -5 -3 5 -2 -1 Using the spreadsheet below (double-click the spreadsheet to open it), verify whether matrix B is the inverse of matrix A. Follow these steps to find the product: Enter the matrices into the spreadsheet below (this has been done for you). Note that matrix A is in cells A2:C4 and matrix B is in cells E2:G4. Both matrices have three rows and three columns, so the product will also be a 3 × 3 matrix. Highlight a 3 × 3 block of cells where you want your answer to appear. Keeping the cells highlighted, enter this formula: =MMULT (A2:C4, E2:G4) Hold down the Shift and Ctrl keys and simultaneously press Enter. The result will appear in the highlighted cells. Matrix A Matrix B 1 2 3 -40 16 9 2 5 3 13 -5 -3 3 0 8 2 -2 -1 Matrix C = A x B Since the product of A and B is equal to I, the identity matrix, matrix B is the inverse of matrix A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.3: The Inverse Of A Matrix

Problem 68EQ

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To verify whether a matrix B is the inverse of the given matrix A, we need to check whether the product of the two matrices is equal to the identity matrix I. You can use a spreadsheet to find the product of two matrices.

1	2	3
2	5	3
1	0	8

-40	16	9
13	-5	-3
5	-2	-1

Using the spreadsheet below (double-click the spreadsheet to open it), verify whether matrix B is the inverse of matrix A. Follow these steps to find the product:

Enter the matrices into the spreadsheet below (this has been done for you). Note that matrix A is in cells A2:C4 and matrix B is in cells E2:G4.
Both matrices have three rows and three columns, so the product will also be a 3 × 3 matrix. Highlight a 3 × 3 block of cells where you want your answer to appear.
Keeping the cells highlighted, enter this formula: =MMULT (A2:C4, E2:G4)
Hold down the Shift and Ctrl keys and simultaneously press Enter. The result will appear in the highlighted cells.