= 2 1 1-3 5-2 4-2 5 -2 1 3 3-1 -4-2 3 2 4 24 134 1 2 -1 2 7 4 P || 90 RREF(A) 0 = 0-45 0 16 0 0 0 -20 0 18 0 19 90 90 0 45 -45 0 90 45 -45 45 10 10 -5 (a) Describe the associated transformation T: R6 R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. 45 00 0 45 0 0 0 45 0 0 0 0 0 0 -4 41 47 50 40 -25 61 16 0 0 0 0 8 0 0
= 2 1 1-3 5-2 4-2 5 -2 1 3 3-1 -4-2 3 2 4 24 134 1 2 -1 2 7 4 P || 90 RREF(A) 0 = 0-45 0 16 0 0 0 -20 0 18 0 19 90 90 0 45 -45 0 90 45 -45 45 10 10 -5 (a) Describe the associated transformation T: R6 R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. 45 00 0 45 0 0 0 45 0 0 0 0 0 0 -4 41 47 50 40 -25 61 16 0 0 0 0 8 0 0
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 1-3 5-2
-1
1
2
4
3
-
4
-1
1
4-2 5 -2
1
3 -1
3
2-4-2
24
7 4 2
P
=
90
4
90
3
1
0-45
0 16
0
0
0-20
0
18 0 19
90
0 45
45
0
RREF(A)
0 90
45
10
10
-5
-45
-45
-
45 0
0
0 45 0
0
0
0
0 45
0
0
00
-4 41
47
50 40 -25
61 16
0
0
00
(a) Describe the associated transformation T: R6 → R5
(b) Give a basis of the null space of A.
(c) Give a basis for the column space of A.
(d) Represent one column as a linear combination of the other columns.
(e) Give a basis for the Range of T.
(f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0.
(g) Let v = [1, 2, 3, 4, 5]. Write v as a linear combination of the of the basis
vectors in
R6 = Espace (0) + Espace(0)+
8
0
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cafdb60-7d1d-4699-94a3-8fee7de7f9f5%2Ff06592a2-d26e-42ed-b5a8-a9aa894fc26c%2F95uo2lm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1:
=
2 1-3 5-2
-1
1
2
4
3
-
4
-1
1
4-2 5 -2
1
3 -1
3
2-4-2
24
7 4 2
P
=
90
4
90
3
1
0-45
0 16
0
0
0-20
0
18 0 19
90
0 45
45
0
RREF(A)
0 90
45
10
10
-5
-45
-45
-
45 0
0
0 45 0
0
0
0
0 45
0
0
00
-4 41
47
50 40 -25
61 16
0
0
00
(a) Describe the associated transformation T: R6 → R5
(b) Give a basis of the null space of A.
(c) Give a basis for the column space of A.
(d) Represent one column as a linear combination of the other columns.
(e) Give a basis for the Range of T.
(f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0.
(g) Let v = [1, 2, 3, 4, 5]. Write v as a linear combination of the of the basis
vectors in
R6 = Espace (0) + Espace(0)+
8
0
0
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