ANSWER D, E, F Use the fact that matrices A and B are row-equivalent.-2-58 0 -171 3-5 1A =-9 -2133 3 -8777 -13 5-31 01 01-2 00 1 -50 00 1B =30 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.(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}

Answered: Image /qna-images/answer/13d12dc4-fed7-40c5-acdc-e41898b580ef.jpg

e the fact that matrices A and B are row-equivalent. -2 -5 1 3 8 0 -17 -5 1 5 A = -9 -21 33 3 -87 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.

e the fact that matrices A and B are row-equivalent. -2 -5 1 3 8 0 -17 -5 1 5 A = -9 -21 33 3 -87 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.

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

ANSWER D, E, F

Use the fact that matrices A and B are row-equivalent.
-2
-5
8 0 -17
1 3
-5 1
A =
-9 -21
33 3 -87
7
7 -13 5
-3
1 0
1 0
1
-2 0
0 1 -5
0 0
0 1
B =
3
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.
(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}

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