The two matrices A and B are row-equivalent. Ansv justify all of your answers. -4 0 1 7 11 1 -2 C 1 A = -2 -1 1 9. 12 0. 1 В 2 1 3 -5 16 C 4 -8 1 -1 6. -2 C (a) Find the rank of A. (b) Find a basis for the row space of A. (c) Find a basis for the column space of A. (d) Find a basis for the nullspace. ||

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 22CM: The two matrices A and B are row-equivalent. A=[240171112119121213516481162]...
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The two matrices A and B are row-equivalent. Answer the questions below, and
justify all of your answers.
2
-4
1
7
11
1 -2 0 0
3
2
-2
1
12
-5
A =
В
0 1
0 0
-1
2
1
3
-5
16
1
7
4
-8
1
-1
6.
-2
(a) Find the rank of A.
(b) Find a basis for the row space of A.
(c) Find a basis for the column space of A.
(d) Find a basis for the nullspace.
(e) Is the last column of A in the span of the first three columns?
(f) Are the first three columns of A linearly independent?
(g) Is the last column of A in the span of columns 1, 3, and 4?
(h) Are the columns 1, 3, and 4 linearly dependent?
Transcribed Image Text:The two matrices A and B are row-equivalent. Answer the questions below, and justify all of your answers. 2 -4 1 7 11 1 -2 0 0 3 2 -2 1 12 -5 A = В 0 1 0 0 -1 2 1 3 -5 16 1 7 4 -8 1 -1 6. -2 (a) Find the rank of A. (b) Find a basis for the row space of A. (c) Find a basis for the column space of A. (d) Find a basis for the nullspace. (e) Is the last column of A in the span of the first three columns? (f) Are the first three columns of A linearly independent? (g) Is the last column of A in the span of columns 1, 3, and 4? (h) Are the columns 1, 3, and 4 linearly dependent?
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