Question: * 7 Theorem: Suppose that A is a p x p nonsingular matrix. Then the cost of computing the LU-decomposition A = P LU of

* 7 Theorem: Suppose that A is a p x p nonsingular matrix. Then the cost of computing the LU-decomposition A = P LU of A is p3 /3 - p/3 multiplications/divisions, and p3 13 - p2 /2 + p/6 additions/subtractions. Use the formulas 1+2+ . . . +n = n(n + 1) 2 and 1+4+ ... +n = n(n + 1)(2n + 1) 6 to prove the theorem

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