Consider the following matrix: -1 9 4 4 2 -2 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 12 *{(CC) 16 6 3) -3 {E]} {]} -2 5) 7 -8 • (GB) {[ 12 -8 2 -6 -13 8 26 16 4 4 0 4 A
Consider the following matrix: -1 9 4 4 2 -2 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 12 *{(CC) 16 6 3) -3 {E]} {]} -2 5) 7 -8 • (GB) {[ 12 -8 2 -6 -13 8 26 16 4 4 0 4 A
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
![Consider the following matrix:
\[
A = \begin{bmatrix}
4 & -1 & 9 \\
4 & 4 & 4 \\
0 & 2 & -2
\end{bmatrix}
\]
Determine which of the following sets of vectors are bases of the column space of \( A \).
1) \(\begin{Bmatrix} \begin{bmatrix} -3 \\ -4 \\ 0 \end{bmatrix} \end{Bmatrix}\)
2) \(\begin{Bmatrix} \begin{bmatrix} 3 \\ -2 \\ 4 \end{bmatrix} \end{Bmatrix}\)
3) \(\begin{Bmatrix} \begin{bmatrix} 12 \\ -1 \\ -6 \end{bmatrix}, \begin{bmatrix} -1 \\ -16 \\ -6 \end{bmatrix} \end{Bmatrix}\)
4) \(\begin{Bmatrix} \begin{bmatrix} 7 \\ 12 \\ 2 \end{bmatrix}, \begin{bmatrix} -8 \\ 1 \\ -4 \end{bmatrix} \end{Bmatrix}\)
5) \(\begin{Bmatrix} \begin{bmatrix} -13 \\ -8 \\ 2 \end{bmatrix}, \begin{bmatrix} 26 \\ 16 \\ -4 \end{bmatrix} \end{Bmatrix}\)
6) \(\begin{Bmatrix} \begin{bmatrix} 8 \\ 6 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 3 \\ -2 \end{bmatrix} \end{Bmatrix}\)
7) \(\begin{Bmatrix} \begin{bmatrix} -3 \\ -1 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ -1 \\ -2 \end{bmatrix} \end{Bmatrix}\)
8) \(\begin{Bmatrix} \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 2 \\ 2 \\ -3 \end{bmatrix} \end{Bmatrix}\)
9) \(\begin{Bmatrix} \begin{bmatrix} 1 \\ 1 \\ -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb493ecdd-cbdc-400d-a05a-de2010eb2d52%2Fd48f3110-7208-45dc-81d5-b67976d62f60%2Fn1auuq2_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following matrix:
\[
A = \begin{bmatrix}
4 & -1 & 9 \\
4 & 4 & 4 \\
0 & 2 & -2
\end{bmatrix}
\]
Determine which of the following sets of vectors are bases of the column space of \( A \).
1) \(\begin{Bmatrix} \begin{bmatrix} -3 \\ -4 \\ 0 \end{bmatrix} \end{Bmatrix}\)
2) \(\begin{Bmatrix} \begin{bmatrix} 3 \\ -2 \\ 4 \end{bmatrix} \end{Bmatrix}\)
3) \(\begin{Bmatrix} \begin{bmatrix} 12 \\ -1 \\ -6 \end{bmatrix}, \begin{bmatrix} -1 \\ -16 \\ -6 \end{bmatrix} \end{Bmatrix}\)
4) \(\begin{Bmatrix} \begin{bmatrix} 7 \\ 12 \\ 2 \end{bmatrix}, \begin{bmatrix} -8 \\ 1 \\ -4 \end{bmatrix} \end{Bmatrix}\)
5) \(\begin{Bmatrix} \begin{bmatrix} -13 \\ -8 \\ 2 \end{bmatrix}, \begin{bmatrix} 26 \\ 16 \\ -4 \end{bmatrix} \end{Bmatrix}\)
6) \(\begin{Bmatrix} \begin{bmatrix} 8 \\ 6 \\ 3 \end{bmatrix}, \begin{bmatrix} 1 \\ 3 \\ -2 \end{bmatrix} \end{Bmatrix}\)
7) \(\begin{Bmatrix} \begin{bmatrix} -3 \\ -1 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ -1 \\ -2 \end{bmatrix} \end{Bmatrix}\)
8) \(\begin{Bmatrix} \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 2 \\ 2 \\ -3 \end{bmatrix} \end{Bmatrix}\)
9) \(\begin{Bmatrix} \begin{bmatrix} 1 \\ 1 \\ -
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