Question: Please help all these problems, thank you for your help. Will rate and review. 10. Let A be the matrix given as 1/2 1/3 1/5

Please help all these problems, thank you for your help. Will rate and review.

10. Let A be the matrix given as 1/2 1/3 1/5 2 0 19 1/5 A = 1/2 -1/3 0 3 1/2 1/3 -1/5 0 0 O 1/2 -1/3 -1/5 Find the matrix B, such ant rank(B, ) = 1 and ||A - Bill2 is minimum, and find the matrix By such ant rank( B2) = 2 and ||A - B2|2 is minimum. 11. Let A c Rox" be a nonsingular matrix. If B is a singular matrix, show that IA - B| |2 2 K2 (A) where *2(A) is the condition number of A for the 2-norm. 12. Let A c Rmxa be a matrix with singular values of 2 02 2 ... and the right singular vectors 11, 12, . .. respectively. Show that 02 = max OATER

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