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 stepbystep. (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) (1 point) Find A'l. Show your work stepbystep. 7T . 3'31 _ - 7 (F) (1 pomt) Solve the system A [$2] [M5] for :02 us1ng Cramer s Rule

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