-3 1 2 -4 1 2 - 9 1 4 Given that A and B 41 -4 -18 find two elementary matrices C and D so -30 1 3 1 that B = CDA.
-3 1 2 -4 1 2 - 9 1 4 Given that A and B 41 -4 -18 find two elementary matrices C and D so -30 1 3 1 that B = CDA.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Given matrices:
\[ A = \begin{bmatrix} -3 & 1 & 2 \\ -4 & 1 & 2 \\ -3 & 0 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} -9 & 1 & 4 \\ 41 & -4 & -18 \\ -3 & 0 & 1 \end{bmatrix} \]
Find two elementary matrices \( C \) and \( D \) such that \( B = CDA \).
**Solution:**
- Matrix \( C \) is defined as a 3x3 matrix:
\[ C = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix} \]
- Matrix \( D \) is also a 3x3 matrix:
\[ D = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix} \]
**Explanation:**
The task is to fill in the blanks for matrices \( C \) and \( D \) with numbers such that when \( C \) is multiplied by \( D \), and then the result is multiplied by \( A \), it equals matrix \( B \). The matrices \( C \) and \( D \) are elementary, meaning they result from performing elementary row operations on the identity matrix. These matrices will help transform \( A \) to \( B \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5025798a-663c-4f82-a82a-d0677c58328a%2F31d40607-462b-469e-9b8f-eaf5855ad453%2Fbx5j8v5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given matrices:
\[ A = \begin{bmatrix} -3 & 1 & 2 \\ -4 & 1 & 2 \\ -3 & 0 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} -9 & 1 & 4 \\ 41 & -4 & -18 \\ -3 & 0 & 1 \end{bmatrix} \]
Find two elementary matrices \( C \) and \( D \) such that \( B = CDA \).
**Solution:**
- Matrix \( C \) is defined as a 3x3 matrix:
\[ C = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix} \]
- Matrix \( D \) is also a 3x3 matrix:
\[ D = \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix} \]
**Explanation:**
The task is to fill in the blanks for matrices \( C \) and \( D \) with numbers such that when \( C \) is multiplied by \( D \), and then the result is multiplied by \( A \), it equals matrix \( B \). The matrices \( C \) and \( D \) are elementary, meaning they result from performing elementary row operations on the identity matrix. These matrices will help transform \( A \) to \( B \).
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