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. A = 3-4 4 15 -9 -2 3 12 -9 2 4 5-2 -4 1 5 4 -2-6 The dimension of Col A is 2 A basis for Col A is given by. (Use a comma to separate vectors as needed.) 1 3-4 4 2 0 0 1-2 0 00 0 0-4 00 0 The dimension of Nul A is A basis for Nul A is given by. (Use a comma to separate vectors as needed.) 0 0
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. A = 3-4 4 15 -9 -2 3 12 -9 2 4 5-2 -4 1 5 4 -2-6 The dimension of Col A is 2 A basis for Col A is given by. (Use a comma to separate vectors as needed.) 1 3-4 4 2 0 0 1-2 0 00 0 0-4 00 0 The dimension of Nul A is A basis for Nul A is given by. (Use a comma to separate vectors as needed.) 0 0
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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![**Task: 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.**
\[ A = \begin{pmatrix}
1 & 3 & -4 & 4 & 2 \\
5 & 15 & -9 & -2 & 3 \\
4 & 12 & -9 & 2 & 4 \\
-2 & -6 & 5 & -2 & -4
\end{pmatrix} \sim \begin{pmatrix}
1 & 3 & -4 & 4 & 2 \\
0 & 0 & 1 & -2 & 0 \\
0 & 0 & 0 & 0 & -4 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix} \]
- - -
### Basis and Dimension of Col A
**A basis for Col A is given by** \(\left\{ \right\}\).
(Use a comma to separate vectors as needed.)
**The dimension of Col A is** \(\).
### Basis and Dimension of Nul A
**A basis for Nul A is given by** \(\left\{ \right\}\).
(Use a comma to separate vectors as needed.)
**The dimension of Nul A is** \(\).
The matrix \(A\) provided initially is row reduced to its echelon form, from which we can identify the pivot columns and determine the bases and dimensions for the column space (Col A) and the null space (Nul A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2Fdfc2fc73-815d-4e43-9e14-9f4440de567f%2Faxgulpr_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: 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.**
\[ A = \begin{pmatrix}
1 & 3 & -4 & 4 & 2 \\
5 & 15 & -9 & -2 & 3 \\
4 & 12 & -9 & 2 & 4 \\
-2 & -6 & 5 & -2 & -4
\end{pmatrix} \sim \begin{pmatrix}
1 & 3 & -4 & 4 & 2 \\
0 & 0 & 1 & -2 & 0 \\
0 & 0 & 0 & 0 & -4 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix} \]
- - -
### Basis and Dimension of Col A
**A basis for Col A is given by** \(\left\{ \right\}\).
(Use a comma to separate vectors as needed.)
**The dimension of Col A is** \(\).
### Basis and Dimension of Nul A
**A basis for Nul A is given by** \(\left\{ \right\}\).
(Use a comma to separate vectors as needed.)
**The dimension of Nul A is** \(\).
The matrix \(A\) provided initially is row reduced to its echelon form, from which we can identify the pivot columns and determine the bases and dimensions for the column space (Col A) and the null space (Nul A).
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