An m ( n matrix A is said to have full rank if rank A = minimum [m, n]. The singular value decomposition lets us measure how close A is to not having full rank. If any singular value is zero, then A does not have full rank. If smin is the smallest singular value of A and smin ( 0, then the distance from A to the set of matrices with rank r = min {m, n} - 1 is smin. Determine the distance from each of the given matrices to the matrices of the same size with rank min{m, n} - 1. (Use MATLAB to find the singular values.)
(a)

(b)

(c)

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