(3) Consider 1 -4 9. -7 1 -1 5 A = -4 1 B = -2 -6 -6 10 7 and assume that the matrix A is row equivalent to B. List rankA and dimNulA, and then find bases of ColA, RowA, and NulA.
(3) Consider 1 -4 9. -7 1 -1 5 A = -4 1 B = -2 -6 -6 10 7 and assume that the matrix A is row equivalent to B. List rankA and dimNulA, and then find bases of ColA, RowA, and NulA.
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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![(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 \(\text{Nul} A\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bd9bd0-40fd-4172-a50a-abb52eb6a8c1%2F34ee32a0-1f19-44fe-8fc3-eb86eb3ed809%2F8ol8dhh_processed.png&w=3840&q=75)
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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