3 1 21 0 0 25110 3 7 2 2 -2 6 13 5 -4 10 10 30-4 01-10 2 0001-2 0 0 0 0 0 (a) Find the rank and nullity of A. rank nullity A = B= (b) Find a basis for the nullspace of A. ↓1 (c) Find a basis for the row space of A. →

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
3
Use the fact that matrices A and B are row-equivalent.
1 21 00
2 51 10
3722-2
6 13 5 4 10
[10 30-4
01-10 2
0001-2
00 0 0 0
(a) Find the rank and nullity of A.
rank
nullity
A =
B=
(b) Find a basis for the nullspace of A.
(c) Find a basis for the row space of A.
↓ 1
(d) Find a basis for the column space of A.
11
-
(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.)
{a₁, a₂, a4}
{a₁, a2, a3)
(a₁, a3, as)
1
→
Transcribed Image Text:3 Use the fact that matrices A and B are row-equivalent. 1 21 00 2 51 10 3722-2 6 13 5 4 10 [10 30-4 01-10 2 0001-2 00 0 0 0 (a) Find the rank and nullity of A. rank nullity A = B= (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. ↓ 1 (d) Find a basis for the column space of A. 11 - (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.) {a₁, a₂, a4} {a₁, a2, a3) (a₁, a3, as) 1 →
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