Solved: Let A = LU, where L is lower triangular with 1s on the diagonal and U is upper

Chapter 7, Problem 9

(choose chapter or problem)

Let A = LU, where L is lower triangular with 1s on the diagonal and U is upper triangular. (a) How many scalar additions and multiplications are necessary to solve Ly = ej by forward substitution? (b) How many additions/subtractions and multiplications/divisions are necessary to solve Ax = ej? The solution xj of Ax = ej will be the jth column of A1. (c) Given the factorization A = LU, how many additional multiplications/divisions and additions/subtractions are needed to compute A1?

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