MATH 235 Midterm: MATH 235 UMass Amherst solution-midterm1
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Fall 2008: (15 points) a) show that the row reduced echelon form of the augmented matrix of the system x1 + x3 x4 2x5 = 2 x1 + x2 + 3x3 = 1. 2x1 + 2x3 + x4 + 5x5 = 1. Clearly write in words each elementary row operation you used. Add r3 to r1: find the general solution for the system. Answer: the free variables are x3 and x5. x1 x2 x3 x4 x5. 1 need to verify this statement: (20 points) you are given that the row reduced echelon form of the matrix. You do not (a) write the general solutions of the system a~x = ~0 in parametric form. ~x = ( rst free variable)~v1 + (second free variable)~v2 + . Answer: the free variables are x2, x5, and x6. x1 x2 x3 x4 x5 x6. 2x2 x5 + x6 x2 x5 x6.
