MATH 2360 Midterm: MATH 2360 TTU Exam 1 Solutions
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. Answer : (x, y, z) = (1, 2, 5) Columns 1,2 and 4 of the coe cent matrix contain leading entries, so x1, x2 and x4 are nonleading variables and x3 and x5 are free variables. I"ll use and for the free parameters, say x3 = , x5 = . Hence, the solution set of the system is parametrized by (x1, x2, x3, x4, x5) = (1 + 2 + , 2 + 3 2 , , 4 5 , ). In each part, solve the linear system using the gauss-jordan method (i. e. , reduce the coe cent matrix to reduced row ech- elon form).
