If E is an elementary matrix for which EA = B where: 1 3 - 3 -3 -1 -1 2 A = 3 2 - 2 - 2 - 2 3 -2 19 3 - 21 - 30 – 18 -1 -1 3 B = 3 – 2 - 2 - 2 3 - 2 then: E = 2. 2. 3. 2.
If E is an elementary matrix for which EA = B where: 1 3 - 3 -3 -1 -1 2 A = 3 2 - 2 - 2 - 2 3 -2 19 3 - 21 - 30 – 18 -1 -1 3 B = 3 – 2 - 2 - 2 3 - 2 then: E = 2. 2. 3. 2.
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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![If \( E \) is an elementary matrix for which \( EA = B \) where:
\[
A = \begin{bmatrix}
1 & 3 & -3 & -3 & 0 \\
3 & -1 & -1 & 2 & 3 \\
-3 & 2 & 2 & 0 & -2 \\
2 & 0 & -2 & -3 & -2
\end{bmatrix}
\]
\[
B = \begin{bmatrix}
19 & 3 & -21 & -30 & -18 \\
3 & -1 & -1 & 2 & 3 \\
-3 & 2 & 2 & 0 & -2 \\
2 & 0 & -2 & -3 & -2
\end{bmatrix}
\]
Then:
\[
E = \begin{bmatrix}
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F200b2eb6-b630-49f4-95ef-5591909fdfea%2F738afca4-7e10-4e35-abc9-56964846ae3b%2Fj4nw83h_processed.png&w=3840&q=75)
Transcribed Image Text:If \( E \) is an elementary matrix for which \( EA = B \) where:
\[
A = \begin{bmatrix}
1 & 3 & -3 & -3 & 0 \\
3 & -1 & -1 & 2 & 3 \\
-3 & 2 & 2 & 0 & -2 \\
2 & 0 & -2 & -3 & -2
\end{bmatrix}
\]
\[
B = \begin{bmatrix}
19 & 3 & -21 & -30 & -18 \\
3 & -1 & -1 & 2 & 3 \\
-3 & 2 & 2 & 0 & -2 \\
2 & 0 & -2 & -3 & -2
\end{bmatrix}
\]
Then:
\[
E = \begin{bmatrix}
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box \\
\Box & \Box & \Box & \Box
\end{bmatrix}
\]
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