Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The B-matrix is - 18 - 5, b₁ = -4 -4 ,b₂= -3 4 b3 4 0
Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The B-matrix is - 18 - 5, b₁ = -4 -4 ,b₂= -3 4 b3 4 0
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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Question
![**Problem Description:**
Find the \( B \)-matrix for the transformation \( x \mapsto Ax \) when \( B = \{ \mathbf{b_1}, \mathbf{b_2}, \mathbf{b_3} \} \).
**Matrix \( A \):**
\[
A = \begin{bmatrix}
-7 & -72 & -18 \\
1 & 17 & 5 \\
-4 & -72 & -21
\end{bmatrix}
\]
**Vectors in Basis \( B \):**
\[
\mathbf{b_1} = \begin{bmatrix} -4 \\ 1 \\ -4 \end{bmatrix}, \quad
\mathbf{b_2} = \begin{bmatrix} -4 \\ 1 \\ -4 \end{bmatrix}, \quad
\mathbf{b_3} = \begin{bmatrix} 4 \\ -1 \\ 0 \end{bmatrix}
\]
**Solution:**
Calculate the \( B \)-matrix based on the given transformation and basis.
**Answer:**
The \( B \)-matrix is \(\boxed{\phantom{answer}}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46029127-96a5-4dc2-997a-3c090d1aab2d%2F8d39b5dd-397f-4c7b-b5f2-98c8307c31e6%2Fkvphl8g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Find the \( B \)-matrix for the transformation \( x \mapsto Ax \) when \( B = \{ \mathbf{b_1}, \mathbf{b_2}, \mathbf{b_3} \} \).
**Matrix \( A \):**
\[
A = \begin{bmatrix}
-7 & -72 & -18 \\
1 & 17 & 5 \\
-4 & -72 & -21
\end{bmatrix}
\]
**Vectors in Basis \( B \):**
\[
\mathbf{b_1} = \begin{bmatrix} -4 \\ 1 \\ -4 \end{bmatrix}, \quad
\mathbf{b_2} = \begin{bmatrix} -4 \\ 1 \\ -4 \end{bmatrix}, \quad
\mathbf{b_3} = \begin{bmatrix} 4 \\ -1 \\ 0 \end{bmatrix}
\]
**Solution:**
Calculate the \( B \)-matrix based on the given transformation and basis.
**Answer:**
The \( B \)-matrix is \(\boxed{\phantom{answer}}\).
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