Question: Suppose A = PtLU, where P is a permutation matrix, L is a lower-triangular matrix with ones on the diagonal, and U is an upper-triangular

Suppose A = PtLU, where P is a permutation matrix, L is a lower-triangular matrix with ones on the diagonal, and U is an upper-triangular matrix.
a. Count the number of operations needed to compute PtLU for a given matrix A.
b. Show that if P contains k row interchanges, then
det P = det Pt = (ˆ’1)k .
c. Use det A = det Pt det L det U = (ˆ’1)k det U to count the number of operations for determining
det A by factoring.
d. Compute det A and count the number of operations when

301520 142002 431231 1114-2 221311 010211

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a To compute P t LU requires 13 n 3 13 n MultiplicationsDivisions and 13 n 3 12 n 2 16 n A... View full answer

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