MATH 235 Midterm: MATH 235 UMass Amherst math235_spring11_html exam1-solution
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Exam 1 solutions (1) (16 points: show that the reduced row echelon form of the augmented matrix of the system x1 + x2 + 2x4 + x5 = 3 x1 x3 + x4 + x5 = 2. 2x1 + 2x3 2x4 x5 = 3 is . Use at most six elementary row operations. (partial credit will be given if you use more). 0: find the general solution of the system. Solution: from the reduced row echelon form of the system, we can see that x3 and x4 are the free variables. Letting x3 = s and x4 = t, we have the general solution: x1 x2 x3 x4 x5 s t + 1. 2 (2) (16 points) let a be a 5 3 matrix (5 rows and 3 columns), ~b, ~c, ~d three vectors in r5 and ~x = x1 x2 x3. You are told that the matrix equation a~x = ~b has a unique solution.
