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
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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f558a7-14fc-4024-84d6-4debb1adc6f6%2F8b50764a-2218-4525-a139-49932bbc0962%2Fummowjc_processed.jpeg&w=3840&q=75)
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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