1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 1 3 3 -1 4 -1 2-4-2 7 2 - 4 P = 90 3 4 1 0-45 0 0 0 18 90 90 RREF(A) 0 16 0 -20 0 19 0 45 -45 45 -45 00 90 45 10 10 -5 - 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
1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 1 3 3 -1 4 -1 2-4-2 7 2 - 4 P = 90 3 4 1 0-45 0 0 0 18 90 90 RREF(A) 0 16 0 -20 0 19 0 45 -45 45 -45 00 90 45 10 10 -5 - 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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Do
d, e, f, g
![1:
=
2
-1
1
2
4
1-3 5-2 1
3 4-2 5 -2
4
3 -1
-
-1
1 3
2-4-2
24
7 4 2
P
=
90
4
3
1
90
RREF(A)
0-45
0 16
0
0
0-20
0
18 0 19
90
0 45
45
00 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%2Fbef0d743-99fb-4d47-a1b4-e3b3785737bb%2Fzhleqml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1:
=
2
-1
1
2
4
1-3 5-2 1
3 4-2 5 -2
4
3 -1
-
-1
1 3
2-4-2
24
7 4 2
P
=
90
4
3
1
90
RREF(A)
0-45
0 16
0
0
0-20
0
18 0 19
90
0 45
45
00 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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