MATH 131 Final: MATH 131 UMass Amherst Umass_FinalExam_2009
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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. 1: 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. Set x3 = t, and solve for the leading variables. There are in nitely many solutions, depending on a single parameter t: x1 x2 x3 x4. 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)
