Use the fact that matrices A and B are row-equivalent. 1 2 10 2 5 1 1 2 2 -2 A = 3 7 19 44 13 4 4 3 0 -4 0 1 -1 0 0 1 -2 0 0 1 0 B = 00 0 0 (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. 2.
Use the fact that matrices A and B are row-equivalent. 1 2 10 2 5 1 1 2 2 -2 A = 3 7 19 44 13 4 4 3 0 -4 0 1 -1 0 0 1 -2 0 0 1 0 B = 00 0 0 (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. 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(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,, a, a3, a4, and as. Which of the following sets is (are) linearly independent? (Select all that apply.)
O {a,, a2, a4}
O {a,, a2, az}
O {a,, a3, as}
Transcribed Image Text:Use the fact that matrices A and B are row-equivalent.
1 2 10
2 5 1 1
2 2 -2
A =
3
7
19 44 13 4
4
3 0 -4
0 1 -1 0
0 1 -2
0 0
1 0
B =
00
0 0
(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.
2.
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