(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 $\text{Nul} A$.

Answered: Image /qna-images/answer/34ee32a0-1f19-44fe-8fc3-eb86eb3ed809.jpg

Answered: (3) Consider 1 -4 9. -7 1 -1 5 A = -4 1…

(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 $\text{Nul} A$.

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