only c,d,e,f Use the fact that matrices A and B are row-equivalent.1 2 1 02 5 1 12 2 -2A =3 719 44 13 441 03 0 -40 1 -1 00 0 0 1 -20 0 0 0B =(a) Find the rank and nullity of A.3nullity 2rank(b) Find a basis for the nullspace of A.341-212. (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 a, a2, az, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.)O {a,, a2, a4}O {a1, a2, az}O {a1, a3, as}

Answered: Image /qna-images/answer/5ec7c1ff-a424-4473-96b3-4c22046ef3e7.jpg

Use the fact that matrices A and B are row-equivalent. 1 2 1 0 2 5 1 1 2 2 -2 A = 3 7 19 44 13 4 4 1 0 3 0 -4 0 1 -1 0 0 0 0 1 -2 0 0 0 0 B = (a) Find the rank and nullity of A. 3 nullity 2 rank (b) Find a basis for the nullspace of A. 3 4 1 -2 1 2.

Use the fact that matrices A and B are row-equivalent. 1 2 1 0 2 5 1 1 2 2 -2 A = 3 7 19 44 13 4 4 1 0 3 0 -4 0 1 -1 0 0 0 0 1 -2 0 0 0 0 B = (a) Find the rank and nullity of A. 3 nullity 2 rank (b) Find a basis for the nullspace of A. 3 4 1 -2 1 2.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 51EQ

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Question

only c,d,e,f

Use the fact that matrices A and B are row-equivalent.
1 2 1 0
2 5 1 1
2 2 -2
A =
3 7
19 44 13 4
4
1 0
3 0 -4
0 1 -1 0
0 0 0 1 -2
0 0 0 0
B =
(a) Find the rank and nullity of A.
3
nullity 2
rank
(b) Find a basis for the nullspace of A.
3
4
1
-2
1
2.

(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 a, a2, az, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a,, a2, a4}
O {a1, a2, az}
O {a1, a3, as}

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