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Math 314 - Fall 2006 Name Quiz 3 1. Let A be the 3 × 3 matrix such that Aij = i + j. Compute AB where 0 1 1 0 . B= 1 0 0 −1 −1 Are the rows of B linearly dependent? 2. Let C the following matrix 1 3 0 0 C= a 1 1 0 0 0 c d (a) What value a has to have to make C an echelon form? (b) Let a = 0 in C. Assume that such a matrix is an echelon form of some matrix A. What value of c and d so that rank(A) = 2? (c) Let d = 1 and c = 1 and a = 0 in the matrix C. Assume that the matrix you obtain is the reduced echelon form of some matrix A. Write the last column of A as linear combination of the first three columns of A. 1