Question: Let M(n) be the time to multiply two n n matrices, and let L(n) be the time to compute the LUP decomposition of an

Let M(n) be the time to multiply two n × n matrices, and let L(n) be the time to compute the LUP decomposition of an n × n matrix( Show that multiplying matrices and computing LUP decompositions of matrices have essentially the same difficulty: an M(n)-time matrix-multiplication algorithm implies an O(M(n))-time LUP-decomposition algorithm, and an L(n)-time LUP-decomposition algorithm implies an O(L(n))-time matrix-multiplication algorithm.

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