Use the fact that matrices A and B are row-equivalent.12 102 5 11 03 7 2 2 -2A =14 32 10 241 030 -40 1 -1 02B =0 0 0 1 -20 0 0 0 O(a) Find the rank and nullity of A.гanknullity(b) Find a basis for the nullspace of A.(©) 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,az, ag, and aş. Which of the following sets is (are) linearly independent? (Select all that apply.)O {a, az, a4}O {a,, az, az}O {a,, az, as}

The solution for the two follows as: Since A and B are row equivalent they have same rank and…

se the fact that matrices A and B are rov-equivalent. 1 2 10 0 25 1 1 0 3 7 22 -2 14 32 10 2 10 30 -4 4 B =01 -1 O 2 0 o 0 1 -2 00 0 0 o (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.

se the fact that matrices A and B are rov-equivalent. 1 2 10 0 25 1 1 0 3 7 22 -2 14 32 10 2 10 30 -4 4 B =01 -1 O 2 0 o 0 1 -2 00 0 0 o (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 23EQ

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Question

Use the fact that matrices A and B are row-equivalent.
1
2 10
2 5 11 0
3 7 2 2 -2
A =
14 32 10 2
4
1 0
30 -4
0 1 -1 0
2
B =
0 0 0 1 -2
0 0 0 0 O
(a) Find the rank and nullity of A.
гank
nullity
(b) Find a basis for the nullspace of A.
(©) 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,
az, ag, and aş. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a, az, a4}
O {a,, az, az}
O {a,, az, as}

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