Given Enter the matrix A in MATLAB and compute its singular values by setting s svd(A) (a) To obtain the full singular value decomposition of A, set U, D, V svd(A) Compute the closest matrix of rank 1 to A by setting B s(1) U( , 1) V( , 1) Ecirc sup1 How are the row vectors of B related to the two distinct row vectors of A (b) The matrices A and B should have the same 2 norm Why Explain Use MATLAB to compute B 2 and B F In general, for a rank 1 matrix the 2 norm and the Frobenius norm should be equal Why Explain 2266 5533

Question: Given Enter the matrix A in MATLAB and compute its singular values by setting s = svd(A). (a) To obtain the full singular value decomposition

Given

Enter the matrix A in MATLAB and compute its singular values by setting s = svd(A).
(a) To obtain the full singular value decomposition of A, set
[U, D, V]= svd(A)
Compute the closest matrix of rank 1 to A by setting
B = s(1) * U(:, 1) * V(:, 1)Ê¹
How are the row vectors of B related to the two distinct row vectors of A?
(b) The matrices A and B should have the same 2-norm. Why? Explain. Use MATLAB to compute ||B||2 and ||B||F. In general, for a rank 1 matrix the 2-norm and the Frobenius norm should be equal. Why? Explain.

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