12. Let u and v be column vectors of length n. Define A = square matrix...

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12. Let u and v be column vectors of length n. Define A = square matrix of order n x n. (a) Give the general element Ai,j. What is the cost in number of operations to create A from u and u in the computer? (b) uvT and note that A is a (c) What is the operations cost of evaluating Ax, where x is a general column vector of length n? Give an alternative and less costly way, in operations, to evaluate Ax = (uvT)x. 12. Let u and v be column vectors of length n. Define A = square matrix of order n x n. (a) Give the general element Ai,j. What is the cost in number of operations to create A from u and u in the computer? (b) uvT and note that A is a (c) What is the operations cost of evaluating Ax, where x is a general column vector of length n? Give an alternative and less costly way, in operations, to evaluate Ax = (uvT)x.

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a The general element Aij of the matrix A uvT is given by the product of the i th element of u and t... View the full answer