Question: Q 1 Consider the matrix A = [32 152] . (A) (1 point) Explain why A is symmetric positive denite (see the denition given in

Q 1 Consider the matrix A = [32 152] . (A) (1 point) Explain why A is symmetric positive denite (see the denition given in class). (B) (1 point) Write the LU factorization of A. Show your work step-by-step. (C) (1 point) If possible, write A as L1DU1, where D is a diagonal matrix, L1 is upper triangular, U1 is lower triangular, and the main diagonal entries of L1 and U1 are 1. Show your work step-by-step. ( (D) 1 point) If possible, write A as Lng, where L2 is lower triangular. [Note: the diagonal entries of L2 need not be 1.] Show your work stepbystep. (E) 71' ( . 331 _ - a (F) (1 p01nt) Solve the system A [$2] [V5] for :62 using Cramer s Rule. 1 point) Find A'l. Show your work stepbystep

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