Question: Problem 1. (15 points) (a) Show that an elementary lower triangular matrix of type k defined by MR (refer lecture notes for the explicit definition

Problem 1. (15 points) (a) Show that an elementary lower triangular matrix of type k defined by MR (refer lecture notes for the explicit definition of this matrix) MK = I+ me (b) Show that the inverse of MR in (a) is given by M = I -mek (c) Show that the elementary matrix M defined in the lecture notes is such that Ma, where a = [a11, a21, . .., ani] , is a multiple of e1

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