Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces. 1 4 3 -8 1 4 3 3 12 1 0 0 4 -7 A = 2 8 - 1 0 0 0 4 4 16 13 0 0 0 1 - 8 1 7 A basis for Col A is given by { - 1 13 (Use a comma to separate answers as needed.) The dimension of Col A is 3. (Type an integer.) A basis for Nul A is given by { }. (Use a comma to separate answers as needed.)

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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Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces.
1
4
- 8
1 4 3
2
3 12
1
7
0 0 4
- 7
A =
8
- 1
9.
0 0 0
4
4 16
13
0 0 0
...
1
- 8
1
7
A basis for Col A is given by
- 1
9.
4
13
(Use a comma to separate answers as needed.)
The dimension of Col A is 3 . (Type an integer.)
A basis for Nul A is given by {
(Use a comma to separate answers as needed.)
Transcribed Image Text:Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces. 1 4 - 8 1 4 3 2 3 12 1 7 0 0 4 - 7 A = 8 - 1 9. 0 0 0 4 4 16 13 0 0 0 ... 1 - 8 1 7 A basis for Col A is given by - 1 9. 4 13 (Use a comma to separate answers as needed.) The dimension of Col A is 3 . (Type an integer.) A basis for Nul A is given by { (Use a comma to separate answers as needed.)
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