Use the fact that matrices A and B are row-equivalent. 1 21 0 2 51 1 3 7 2 6 13 5-1 10 3 0 -4 0 1 -1 0 2 0 0 2 -2 4 0 1 -2 0 0 00 (a) Find the rank and nullity of A. rank nullity (h) Find a basis for the nuullspace of A

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
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(e) Determine whether or not the rows of A are linearly independent.
O independent
O dependent
() Let the columns of A be denoted by a, az, az, ag, and as. 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)
Transcribed Image Text:(e) Determine whether or not the rows of A are linearly independent. O independent O dependent () Let the columns of A be denoted by a, az, az, ag, and as. 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)
Use the fact that matrices A and B are row-equivalent.
[1 21 0
2 51 1 0
3 7 2 2-2
6 13 5 -1
[10 30 -4
4
2
B-01 -1 0
0 0 0 1 -2
0 0 00
(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.
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent. [1 21 0 2 51 1 0 3 7 2 2-2 6 13 5 -1 [10 30 -4 4 2 B-01 -1 0 0 0 0 1 -2 0 0 00 (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.
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