8. Let A be a matrix whose singular value decomposition is given by 2 -1/ ---/ -/3/ 100 0 -/-/ 2-12 20 CTIN -2/3 - 2/3 98 2/5 325 QUO 0 0 0 0 0 10 0 0 10 0 0 0 0 0 12 -1/2 -1/2 5 0 0 0 Make use of the singular value decomposition to do each of the following. (a) Determine the rank of A. (b) Find an orthonormal basis for C(A). (c) Find an orthonormal basis for N(A). (d) Find an orthonormal basis for C(AT). (e) Find an orthonormal basis for N(AT). (f) Find the closest rank 1 matrix B to A. 72 72 1 -1/2 3 -1/2 -1/1 72 FIN 1 2 دمات (g) Use the singular value decomposition of A to compute the distance between A and B with respect to the Frobenius norm.
8. Let A be a matrix whose singular value decomposition is given by 2 -1/ ---/ -/3/ 100 0 -/-/ 2-12 20 CTIN -2/3 - 2/3 98 2/5 325 QUO 0 0 0 0 0 10 0 0 10 0 0 0 0 0 12 -1/2 -1/2 5 0 0 0 Make use of the singular value decomposition to do each of the following. (a) Determine the rank of A. (b) Find an orthonormal basis for C(A). (c) Find an orthonormal basis for N(A). (d) Find an orthonormal basis for C(AT). (e) Find an orthonormal basis for N(AT). (f) Find the closest rank 1 matrix B to A. 72 72 1 -1/2 3 -1/2 -1/1 72 FIN 1 2 دمات (g) Use the singular value decomposition of A to compute the distance between A and B with respect to the Frobenius norm.
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:8. Let A be a matrix whose singular value decomposition is given by
2
100
0
-/-/
2-1
25
TIN
350
GIN
²
-2/3-2/3
998
5
232323
-12-1/
-1/2
0
0 0
Make use of the singular value decomposition to do each of the following.
(a) Determine the rank of A.
(b) Find an orthonormal basis for C(A).
(c) Find an orthonormal basis for N(A).
(d) Find an orthonormal basis for C(AT).
(e) Find an orthonormal basis for N(AT).
(f) Find the closest rank 1 matrix B to A.
(g) Use the singular value decomposition of A to compute the distance between A and B with
respect to the Frobenius norm.
2/5
0
QUO
0
0
10
0
0
0
0
0 10
0
0
12
0 0
12
21
-1/2 -
1/1/201
12
TIN
21
2
دمات
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