(d) Find a basis for the column space of A.(e) Determine whether or not the rows of A are linearly independent.O independentdependent(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}{a1, a2, a3}{a1, a3, a5} Use the fact that matrices A and B are row-equivalent.12 12A =35 117 22 -27 15 6 -141 030 -40 1 -1 0B =0 00 1 -20 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.

The given matrix is A=12100251103722-27156-14 and B=1030-401-1020001-200000…

Answered: Use the fact that matrices A and B are…

Use the fact that matrices A and B are row-equivalent. 2 1 2 5 1 7 2 1 A = 2 -2 7 15 6 -1 3 0 -4 0 1 -1 0 0 1 -2 0 0 4 1 0 2 B = 0 0 0 0 (a) Find the rank and nullity of A.

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
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}
{a1, a2, a3}
{a1, a3, a5}

Use the fact that matrices A and B are row-equivalent.
1
2 1
2
A =
3
5 1
1
7 2
2 -2
7 15 6 -1
4
1 0
30 -4
0 1 -1 0
B =
0 0
0 1 -2
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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