Question: Need help with diffeq (6pts) Consider the matrix A = NO (a) Find A1, an optimal rank-one approximation of A. (b) Use theorem 2 from

Need help with diffeq

(6pts) Consider the matrix A = NO (a) Find A1, an optimal rank-one approximation of A. (b) Use theorem 2 from lecture 7 to calculate rank(A), rank(A1), rank(A - A1), I|All, IAlll, and ||A - Alll. Theorem 2: Let A in Rmxn where rank(A) = r 2 1 and suppose A" A has eigenvalues *1 2 12 2 .. . 2 An 20 (5) Suppose that AT Avi = Aivi where (v1|| = 1 and set A1 = Aviv]. Then 1. rank(A1) = 1 and rank(A - Al) = r - 1 2. || Alll = 1All = VAI and ||A - Alll = VA2 3. If B1 is any matrix in Rmxn such that rank(B1) = 1, then ||A - Alll

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