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 equivalent echelon form of matrix A is given to make your work easier. [4 4 22 31 [100]

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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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 equivalent echelon form of
matrix A is given to make your work easier.
4 22 3
[1 0 01
3
1
0
0
1 0
1 3
~
0
01
2
4
-1
0
0 0
-6 10
4
[000
A=-6
Basis for the column space of A is
Basis for the row space of A is
9.
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 equivalent echelon form of matrix A is given to make your work easier. 4 22 3 [1 0 01 3 1 0 0 1 0 1 3 ~ 0 01 2 4 -1 0 0 0 -6 10 4 [000 A=-6 Basis for the column space of A is Basis for the row space of A is 9.
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