MAT223H1 Study Guide - Midterm Guide: Elementary Matrix, Euclidean Vector, Linear Combination
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October 22, 2009: kim, s. kudla, f. murnaghan, s. uppal. Find all solutions of the homogeneous linear system ax = 0, where a is a 3 6 matrix whose reduced row echelon form is 1 2 0 3 0 5. The reduced row echelon form of a has 3 leading ones, so we will assign three param- eters to non-leading variables : x2 = s, x4 = t, x6 = u. From the last row we can see that x5 = u. The second row sais that x3 + 4x4 + 6x6 = 0 x3 = 4t 6u. The third row means that x1 + 2x2 + 3x4 + 5x6 = 0 x1 = 2s 3t 5u. Thus all the solutions x = (x1, x2, x3, x4, x5, x6)t of the homogeneous linear system. Find a 2 2 matrix a such that. We nd a by nding inverse of the matrix(cid:18) 1.
