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 3 -4 3 19 3 1 0 0 5 2 00 1 000 00 -2 1001 0 1 6 -2 -4 11 6 Basis for the column space of Ais 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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
3
-4
3
19 3
10 01
1
0
0 1 0
5 2 00 1
0 0 0
-2
6
-2
11 6
Basis for the column space of A is
Basis for the row space of A is
00
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 equivalent echelon form of matrix A is given to make your work easier. 4 3 -4 3 19 3 10 01 1 0 0 1 0 5 2 00 1 0 0 0 -2 6 -2 11 6 Basis for the column space of A is Basis for the row space of A is 00 Note that since the only solution to Ax= 0 is the zero vector, there is no basis for the null space of A
Let
Give a non-zero vector in the null space of A.
a ==
A-4 -4
3
5
-2
-3 -1
2
4
Transcribed Image Text:Let Give a non-zero vector in the null space of A. a == A-4 -4 3 5 -2 -3 -1 2 4
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