MATH 131 Midterm: MATH 131 UMass Amherst Umass_2014 Exam
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Spring 2005: 7 points use gauss-jordan elimination to solve the following system of equations. bf indicate for each step which row operation you use. Carry out the elimination all the way (to rref form) before solving. 2x + 2y + 9z = 7 y + 5z = 2: 8 points consider the following system of linear equations: x1. Identify which variables are leading and which are free. Write down the general solution of the system, in vector form. Spring 2005: 6 points the reduced row echelon forms of the augmented matrices of 3 systems are given below. In each case, indicate the rank of the matrix of coe cients (to the left of the dotted lines), and the number of solutions of the system (you need not write down the solutions. ) (a) 0: 3 points find the matrix a of the linear transformation t : r5.
