2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0.4 0.4 0 0 0 0 A = 0.4 0.4 0.6 0.5 0.5 0.5 0.5] 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm.
2. Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0 0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0 -0.4 0.6 -0.4 -0.4 0 0 10 0 0.6 -0.4 -0.4 -0.4 0 0 0 0 0.4 0.4 0.4 0.4 0 0 0 0 A = 0.4 0.4 0.6 0.5 0.5 0.5 0.5] 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 -0.5 0.5 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of ATA. (d) Find the orthonormal basis for R(A). (e) Find the orthonormal basis for N(A). (f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and B using the Frobenius norm.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![2. Let A be a matrix whose singular value decomposition is given by
[0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0
0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0
A = 0.4 -0.4 0.6 -0.4 -0.4 0 0 10 0
0.6 -0.4 -0.4 -0.4 0 0 0 0
0.4 0.4 0 0 0 0
0.4
0.6
0.4 0.4
0.5 0.5 0.5]
0.5
0.5 -0.5 -0.5 0.5
-0.5 -0.5 0.5 0.5
-0.5 0.5 -0.5 0.5
(a) Find A.
(b) Determine rank of A.
(c) Find eigenvalues of ATA.
(d) Find the orthonormal basis for R(A).
(e) Find the orthonormal basis for N(A).
(f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and
B using the Frobenius norm.
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c9872f4-07a5-438e-9711-8d7455ed4876%2F1ee85e89-19a2-460f-a600-7da824669d19%2Fl8x3sba_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let A be a matrix whose singular value decomposition is given by
[0.4 -0.4 -0.4 -0.4 0.6 [100 0 0 0
0.4 -0.4 -0.4 0.6 -0.4 0 10 0 0
A = 0.4 -0.4 0.6 -0.4 -0.4 0 0 10 0
0.6 -0.4 -0.4 -0.4 0 0 0 0
0.4 0.4 0 0 0 0
0.4
0.6
0.4 0.4
0.5 0.5 0.5]
0.5
0.5 -0.5 -0.5 0.5
-0.5 -0.5 0.5 0.5
-0.5 0.5 -0.5 0.5
(a) Find A.
(b) Determine rank of A.
(c) Find eigenvalues of ATA.
(d) Find the orthonormal basis for R(A).
(e) Find the orthonormal basis for N(A).
(f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A and
B using the Frobenius norm.
1
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