Question: Suppose A = S?S?1, where ? is a diagonal matrix with diagonal elements ?1,...,?n. Write S = s1 sn ; that is, si is the

Suppose A = S?S?1, where ? is a diagonal matrix with diagonal elements ?1,...,?n. Write S = s1 sn ; that is, si is the ith column of S.

3. Suppose A = SAS-1, where A is a diagonal matrix with diagonal elements )1, ..., An. Write S = $1 ... Sn ; that is, Si is the ith column of S. (a) Show that Asi = Misi for i = 1, ..., n. (b) Show that if x = als1 + a252 + . .. + ansn, then A*x = aldis1 + azizs2 + ... + andrisn. (c) Suppose Wil

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