(d) Find a basis for the column space of A.(e) Determine whether or not the rows of A are linearly independent.O independentO dependent(f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.)O {a1, a2, a4}O {a1, a2, a3}O {a1, a3, a5} Use the fact that matrices A and B are row-equivalent.-2 -58 0 -1713-5 1A =-3 -57 5 -4317 -13 5-31 01 010 1 -2 03B =0 00 1 -50 00 0(a) Find the rank and nullity of A.ranknullity(b) Find a basis for the nullspace of A.(c) Find a basis for the row space of A.

Answered: Image /qna-images/answer/f09ab853-fe5e-460f-b8e7-7b3acfdb688f.jpg

Answered: ) Determine whether or not the rows of…

) Determine whether or not the rows of A are linearly indepen O independent O dependent Let the columns of A be denoted by a,, a2, a3, a4, and as. V O {a,, a2, a4} O {a,, a2, az} O {a,, a3, as}

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 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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Question

(d) Find a basis for the column space of A.
(e) Determine whether or not the rows of A are linearly independent.
O independent
O dependent
(f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a1, a2, a4}
O {a1, a2, a3}
O {a1, a3, a5}

Use the fact that matrices A and B are row-equivalent.
-2 -5
8 0 -17
1
3
-5 1
A =
-3 -5
7 5 -43
1
7 -13 5
-3
1 0
1 0
1
0 1 -2 0
3
B =
0 0
0 1 -5
0 0
0 0
(a) Find the rank and nullity of A.
rank
nullity
(b) Find a basis for the nullspace of A.
(c) Find a basis for the row space of A.

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