Use the fact that matrices A and 8 are row-equivalent. 2 10 0 5 11 0 722-2 A = B = 1 2 3 10 23 7 0 10 30-4 0 1-1 0 2 0001-2 00 00 0 nullity 6 (a) Find the rank and nullity of A. rank (b) Find a basis for the nullspace of A. 11 (c) Find a basis for the row space of A. 000 100 DU (d) Find a basis for the column space of A. t
Use the fact that matrices A and 8 are row-equivalent. 2 10 0 5 11 0 722-2 A = B = 1 2 3 10 23 7 0 10 30-4 0 1-1 0 2 0001-2 00 00 0 nullity 6 (a) Find the rank and nullity of A. rank (b) Find a basis for the nullspace of A. 11 (c) Find a basis for the row space of A. 000 100 DU (d) Find a basis for the column space of A. t
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:Use the fact that matrices A and 8 are row-equivalent.
1
2 1 0 0
2
5
1
0
3 7 22-2
10 23 7 0 6
10 30 -4
0
-1 0 2
0 1 -2
00 0
A =
B=
00
(a) Find the rank and nullity of A.
rank
nullity
(b) Find a basis for the nullspace of A.
11
(c) Find a basis for the row space of A.
(d) Find a basis for the column space of A.
E
11
0 (₂₂₂)
(₂₂)
(e) Determine whether or not the rows of A are linearly independent
O Independen
O dependent
(Let the oclumns of A be denoted by a,, aa a anda. Which of the following sets is (are) linearly incepandent? (Select all that apply.)
O{M₂ M₂ M₂)
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