MATH 2360 Midterm: MATH 2360 TTU Exam Solutions 3a
31 Jan 2019
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In each part you are given the augmented matrix of a system of linear equations, with the coe cent matrix in reduced row echelon form. Determine if the system is consistent and, if it is consistent, nd all solutions. The system is inconsistent because of the last row, which has all zeros in the coe cent matrix and a nonzero entry on the right-hand side. There are no free variables and the three rows correspond to the equations z = 5, y = 1 and x = 2. Thus, the system has a unique solution, which is (x, y, z) = ( 2, 1, 5). Then x1, x3 and x5 are leading variables and x2 and x4 are free variables, say x2 = and x4 = . Thus, the system has a two parameter family of solutions given by (x1, x2, x3, x4, x5) = (2 2 , , 1 + , , 5)
