MATH 235 Midterm: MATH 235 UMass Amherst midterm1-solution
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Spring 2014: (20 points) a) show that the row reduced echelon form of the augmented matrix of the system. + x3 x4 + x5 = 1 x1. 3x1 + 2x2 + x3 3x4 x5 = 1 x1 + x2. X4 + x5 = 2 is . Clearly write in words each elementary row operation you used: find the general solution for the system. x1 x2 x3 x4 x5, (15 points) you are given that the row reduced echelon form of the matrix. You do not need to (a) write the general solution of the system a~x = ~0 in parametric form. ~x = ( rst free variable)~v1 + (second free variable)~v2 + (b) let t : r5. R3 be the linear transformation given by t (~x) = a~x. Justify your answer: a) (13 points) determine for which values of k the 3 3 matrix a = .
