Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 3 1 - 9 1 3 10-9 7 4 2 - 18 0 1 2 2 A = - 3 - 12 -9 - 1 37 0 0 0 1 13 11 3 - 37 0 0 0 0 A basis for Col A is given by {}. (Use a comma to separate vectors as needed.) O N

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Linear Algebra.

Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below.

Matrix A:
\[
A = \begin{bmatrix}
1 & 3 & 1 & 0 & -9 \\
2 & 7 & 4 & 2 & -18 \\
-3 & -12 & -9 & -1 & 37 \\
3 & 13 & 11 & 3 & -37
\end{bmatrix}
\]

Echelon form of A:
\[
\sim \begin{bmatrix}
1 & 3 & 1 & 0 & -9 \\
0 & 1 & 2 & 2 & 0 \\
0 & 0 & 0 & 1 & 2 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix}
\]

A basis for Col A is given by [\,].  
(Use a comma to separate vectors as needed.)
Transcribed Image Text:Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. Matrix A: \[ A = \begin{bmatrix} 1 & 3 & 1 & 0 & -9 \\ 2 & 7 & 4 & 2 & -18 \\ -3 & -12 & -9 & -1 & 37 \\ 3 & 13 & 11 & 3 & -37 \end{bmatrix} \] Echelon form of A: \[ \sim \begin{bmatrix} 1 & 3 & 1 & 0 & -9 \\ 0 & 1 & 2 & 2 & 0 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \] A basis for Col A is given by [\,]. (Use a comma to separate vectors as needed.)
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