MATH 21 Study Guide - Midterm Guide: Free Variables And Bound Variables, Linear Combination, Row Echelon Form
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If true, brie y explain why; if false, give a counter-example. (a) if b c(a), then a x = b has exactly one solution. False. (if n (a) is nontrivial, there will be in nitely many solutions. ) E. g. , b = 0 and a the zero matrix. (b) if a is invertible, no permutations are required when computing the lu decomposi- tion of a. And (c) if the only solution of ax = 0 is x = 0, then ax = b always has a unique solution. False. (if b isn"t in c(a), ax = b has no solution. ) 2. (a) express the systems of equations x1 + x2. = 1 x1 + 2 x2 + x3 = 1 x2 + 2 x3 = 1 in matrix vector form, i. e. as a x = b for an appropriate matrix a and vectors x and b. A = (b) find the reduced row echelon form of the matrix a determined in (a).
