Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equi of matrix A is given to make your work easier. 3 2 A = -6 3 26 5 1 0 2 3 7 -3, -6 8 4 0 Basis for the column space of A is 1 0 Basis for the row space of A is 0 1 ][ Note that since the only solution to Ax = 0 is the zero vector, there is no basis for the null space of A.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 77E
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Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equi
of matrix A is given to make your work easier.
26 5
1 0 0
1
0
0
1 0
2
3
0 0
1
3
7
-3
0
0 0
-6 8 4
0
Basis for the column space of A is
A
=
3
2
-6
1
Basis for the row space of A is
{{
"
"
"
Note that since the only solution to Ax
=
0 is the zero vector, there is no basis for the null space of A.
Transcribed Image Text:Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equi of matrix A is given to make your work easier. 26 5 1 0 0 1 0 0 1 0 2 3 0 0 1 3 7 -3 0 0 0 -6 8 4 0 Basis for the column space of A is A = 3 2 -6 1 Basis for the row space of A is {{ " " " Note that since the only solution to Ax = 0 is the zero vector, there is no basis for the null space of A.
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