Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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(3) Consider

\[
A = \begin{pmatrix} 
1 & -4 & 9 & -7 \\ 
-1 & 2 & -4 & 1 \\ 
5 & -6 & 10 & 7 
\end{pmatrix}, \quad 
B = \begin{pmatrix} 
1 & 0 & -1 & 5 \\ 
0 & -2 & 5 & -6 \\ 
0 & 0 & 0 & 0 
\end{pmatrix}
\]

and assume that the matrix \(A\) is row equivalent to \(B\). List \(\text{rank} A\) and \(\dim \text{Nul} A\), and then find bases of \(\text{Col} A\), \(\text{Row} A\), and \(\text{Nul} A\).
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Transcribed Image Text:(3) Consider \[ A = \begin{pmatrix} 1 & -4 & 9 & -7 \\ -1 & 2 & -4 & 1 \\ 5 & -6 & 10 & 7 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 0 & -1 & 5 \\ 0 & -2 & 5 & -6 \\ 0 & 0 & 0 & 0 \end{pmatrix} \] and assume that the matrix \(A\) is row equivalent to \(B\). List \(\text{rank} A\) and \(\dim \text{Nul} A\), and then find bases of \(\text{Col} A\), \(\text{Row} A\), and \(\text{Nul} A\).
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