Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![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 \\ -](https://content.bartleby.com/qna-images/question/b493ecdd-cbdc-400d-a05a-de2010eb2d52/d48f3110-7208-45dc-81d5-b67976d62f60/n1auuq2_processed.png)
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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