Jse the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 1 3 -5 1 5 A = -5 -11 17 3 -53 7 -13 5 -3 10 10 1 0 1 -2 0 00 01 -5 0 0 0 1 3 (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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
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5.

Use the fact that matricesA and B are row-equivalent.
8 0 -17
-5 1
-2
-5
1
3
A =
-5 -11
17 3 -53
1
7 -13 5
-3
1 0
01 -2 0
1 0
3
01 -5
0 0 0
B =
(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
(r) Let the columns of A be denoted by a,
a4, and ag. Which of the following sets is (are) linearly independent? (Select all that apply.)
O (a, a2, a4
O (a az, a3)
O (a, a3, as}
Transcribed Image Text:Use the fact that matricesA and B are row-equivalent. 8 0 -17 -5 1 -2 -5 1 3 A = -5 -11 17 3 -53 1 7 -13 5 -3 1 0 01 -2 0 1 0 3 01 -5 0 0 0 B = (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 (r) Let the columns of A be denoted by a, a4, and ag. Which of the following sets is (are) linearly independent? (Select all that apply.) O (a, a2, a4 O (a az, a3) O (a, a3, as}
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