MATH 235 Midterm: MATH 235 UMass Amherst math235_fall08_html midterm1
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Name: (15 points) a) show that the row reduced echelon form of the augmented matrix of the system x1 + x3 x4 2x5. 2x1 + 2x3 + x4 + 5x5 = 1. Clearly write in words each elementary row operation you used. is . Use at: find the general solution for the system. x1 x2 x3 x4 x5. 1: (20 points) you are given that the row reduced echelon form of the matrix. 1 need to verify this statement. (a) write the general solutions of the system a~x = ~0 in parametric form. ~x = ( rst free variable)~v1 + (second free variable)~v2 + . (b) let t : r6 r4 be the linear transformations given by t (~x) = a~x. Nite set of vectors in ker(t ), which spans ker(t ). Explain why the set you found spans ker(t ). 2 (c) let ~aj be the j-th column of a.
