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Find a matrix A such that the given set W of vectors is the column space Col(A). -r + 3t 2r2s + t 3r+2s 3t -3r+ 3s W O O O A = A = A = || A = 1 3 0 - 1 0 3 -2 2 2 3 3 2 3 -3 3 -3 3 1 -3 0 -1 -2 2 2 -3 33 3 -1 0 2 -3] 0 -2 2 0 3 1 -3 3 -2 1 2 -3 3 0 : r, s, tER

Find a matrix A such that the given set W of vectors is the column space Col(A). -r + 3t 2r2s + t 3r+2s 3t -3r+ 3s W O O O A = A = A = || A = 1 3 0 - 1 0 3 -2 2 2 3 3 2 3 -3 3 -3 3 1 -3 0 -1 -2 2 2 -3 33 3 -1 0 2 -3] 0 -2 2 0 3 1 -3 3 -2 1 2 -3 3 0 : r, s, tER

Advanced Engineering Mathematics
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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Find a matrix \( A \) such that the given set \( W \) of vectors is the column space \(\text{Col}(A)\). \[ W = \left\{ \begin{bmatrix} -r + 3t \\ 2r - 2s + t \\ 3r + 2s - 3t \\ -3r + 3s \end{bmatrix} : r, s, t \in \mathbb{R} \right\} \] Options for matrix \( A \): 1. \[ A = \begin{bmatrix} 1 & 0 & 3 \\ 1 & -2 & 2 \\ -3 & 2 & 3 \\ 0 & 3 & -3 \end{bmatrix} \] 2. \[ A = \begin{bmatrix} 1 & 3 & 0 \\ 2 & 1 & -2 \\ 3 & -3 & 2 \\ 3 & 3 & 0 \end{bmatrix} \] 3. \[ A = \begin{bmatrix} 0 & -1 & 3 \\ -2 & 2 & 1 \\ 2 & 3 & -3 \\ -3 & 3 & 0 \end{bmatrix} \] 4. \[ A = \begin{bmatrix} -1 & 0 & 3 \\ 2 & -2 & 1 \\ 3 & 2 & -3 \\ -3 & 3 & 0 \end{bmatrix} \]
Transcribed Image Text:Find a matrix \( A \) such that the given set \( W \) of vectors is the column space \(\text{Col}(A)\). \[ W = \left\{ \begin{bmatrix} -r + 3t \\ 2r - 2s + t \\ 3r + 2s - 3t \\ -3r + 3s \end{bmatrix} : r, s, t \in \mathbb{R} \right\} \] Options for matrix \( A \): 1. \[ A = \begin{bmatrix} 1 & 0 & 3 \\ 1 & -2 & 2 \\ -3 & 2 & 3 \\ 0 & 3 & -3 \end{bmatrix} \] 2. \[ A = \begin{bmatrix} 1 & 3 & 0 \\ 2 & 1 & -2 \\ 3 & -3 & 2 \\ 3 & 3 & 0 \end{bmatrix} \] 3. \[ A = \begin{bmatrix} 0 & -1 & 3 \\ -2 & 2 & 1 \\ 2 & 3 & -3 \\ -3 & 3 & 0 \end{bmatrix} \] 4. \[ A = \begin{bmatrix} -1 & 0 & 3 \\ 2 & -2 & 1 \\ 3 & 2 & -3 \\ -3 & 3 & 0 \end{bmatrix} \]
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