MAT223H1 Study Guide - Midterm Guide: Row Echelon Form, Augmented Matrix, Identity Matrix
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October 18, 2013: crooks, m. mota, c. park, s. uppal, f. vera-pacheco, y. zong. 1 of 9: suppose that the given matrix is the augmented matrix of a system of linear equations in the variables x1, x2, x3, x4, x5, x6. [6] (a) find the reduced echelon form of the given system. [2] (c) find the set of solutions to the given system. 2 of 9 (b) x2, x5 and x6 are the free variables. (they correspond to columns without leading 1s. ) (c) from our answer to (a), we nd that the solutions are given by. 0 2x2 x5 + x6 x1 x2 x3 x4 x5 x6 x2. A certain 3 3 matrix a has inverse. Find a matrix y such that (ay 4i)t a = c, where c = Solution: let us manipulate the given equation and isolate y : , and i is the (ay 4i)t a = c = ((ay 4i)t a)a 1 = ca 1.
