Find the following matrix product, if it exists.8 -2- 8-3 -719-26 - 14- 5Select the correct choice below and, if necessary, fill in the answer box to complete your choice.8 -2-8- 3-7OA.9- 2(Simplify your answer.)6 - 14-54O B. The product does not exist.

Given expression is 8−2−81096−14−3−7−20−54. We have to find the product of the given matrix.…

Answered: Find the following matrix product, if…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 15EQ: 15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

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Related questions

Question

Find the following matrix product, if it exists.
8 -2
- 8
-3 -7
1
9
-2
6 - 1
4
- 5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
8 -2
-8
- 3
-7
OA.
9
- 2
(Simplify your answer.)
6 - 1
4
-5
4
O B. The product does not exist.

Expert Solution

Step 1

Given expression is $[\begin{matrix} 8 & - 2 & - 8 \\ 1 & 0 & 9 \\ 6 & - 1 & 4 \end{matrix}] [\begin{matrix} - 3 & - 7 \\ - 2 & 0 \\ - 5 & 4 \end{matrix}]$ .

We have to find the product of the given matrix.

$\begin{matrix} [\begin{matrix} 8 & - 2 & - 8 \\ 1 & 0 & 9 \\ 6 & - 1 & 4 \end{matrix}] [\begin{matrix} - 3 & - 7 \\ - 2 & 0 \\ - 5 & 4 \end{matrix}] = [\begin{matrix} 8 (- 3) + (- 2) (- 2) + (- 8) (- 5) & 8 (- 7) + (- 2) (0) + (- 8) (4) \\ 1 (- 3) + (0) (- 2) + (9) (- 5) & 1 (- 7) + (0) (0) + (9) (4) \\ 6 (- 3) + (- 1) (- 2) + (4) (- 5) & 6 (- 7) + (- 1) (0) + (4) (4) \end{matrix}] \\ = [\begin{matrix} - 24 + 4 + 40 & - 56 + 0 - 32 \\ - 3 + 0 - 45 & - 7 + 0 + 36 \\ - 18 + 2 - 20 & - 42 + 0 + 16 \end{matrix}] \\ = [\begin{matrix} 20 & - 88 \\ - 48 & 29 \\ - 36 & - 26 \end{matrix}] \end{matrix}$