9. Find a set of columns that form a basis for the column space of each of the following matrices. Give the rank of each matrix. Also find a basis for the null space of each matrix. (a) [3 -3 5 6 -10 2 1 7 (b) 125 14 1 1 0 (c) 0 0 1 0 0 1 1 0 2 -1 1 10 1 1 1 1 1 2 1 1 0 (d) 102-1 1 01 010 0 1-12 1 1 1 1 1 1 1 02-1 1 1 1 1 1 0 07 1 01 0 10 1 001 10 (e) 0 1 1 01 0 0 1 01 0 01 1 0100 1.
9. Find a set of columns that form a basis for the column space of each of the following matrices. Give the rank of each matrix. Also find a basis for the null space of each matrix. (a) [3 -3 5 6 -10 2 1 7 (b) 125 14 1 1 0 (c) 0 0 1 0 0 1 1 0 2 -1 1 10 1 1 1 1 1 2 1 1 0 (d) 102-1 1 01 010 0 1-12 1 1 1 1 1 1 1 02-1 1 1 1 1 1 0 07 1 01 0 10 1 001 10 (e) 0 1 1 01 0 0 1 01 0 01 1 0100 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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please do 9bc please.
Transcribed Image Text:9. Find a set of columns that form a basis for the column space of each
of the following matrices. Give the rank of each matrix. Also find a
basis for the null space of each matrix.
(a)
[3
-3
5
6 -10
2 1 7
(b)
125
14
1
1 0
(c) 0 0
1 0 0 1
1
0
2 -1 1
10 1
1
1 1
1
2
1 1 0
(d)
102-1
1
01
010
0
1-12 1
1 1 1
1 1
1
02-1 1
1 1 1
1 0 07
1
01 0 10 1
001 10
(e)
0 1
1 01 0
0
1 01 0 01
1
0100
1.
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