/1 5 0 2 0 2 10 1 4 0 9. You are given that the reduced row echelon form of the matrix A = 3 15 6 30 is 1 5 0 2 0 00100 00001 00000 (a) (b) (c) Given this information: Verify the rank-nullity theorem holds in this case. Find a basis for the column space of A. Find a basis for the null space of A. 16 1 2 12 1,

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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1
2
9. You are given that the reduced row echelon form of the matrix A =
3
6
is
1 5 0 2 0
00100
00001
00000/
(a)
(b)
(c)
(d)
Given this information:
Verify the rank-nullity theorem holds in this case.
Find a basis for the column space of A.
Find a basis for the null space of A.
Simplify the expression: span
0
2
2
10
1
4
0
3
15
1
6
5 0 2 0\
10 1 4 0
15 1
6 1
30 2 12 1,
6
30
2
12
Transcribed Image Text:1 2 9. You are given that the reduced row echelon form of the matrix A = 3 6 is 1 5 0 2 0 00100 00001 00000/ (a) (b) (c) (d) Given this information: Verify the rank-nullity theorem holds in this case. Find a basis for the column space of A. Find a basis for the null space of A. Simplify the expression: span 0 2 2 10 1 4 0 3 15 1 6 5 0 2 0\ 10 1 4 0 15 1 6 1 30 2 12 1, 6 30 2 12
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