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.

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