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Math 2250 Week 5 Quiz Name and Unid: SOLUTION Write your answer in the space provided. Show work for full credit. 1. (10 points) Find the row reduced echelon 1 0 −1 Solution: 1 2 1 0 1 −1 −1 1 −4 1 0 0 form of the matrix 2 1 1 −1 . 1 −4 1 2 1 0 1 −1 0 3 −3 R1 + R3 → R3 R1 − 2R2 → R1 2 1 1 1 −1 0 0 0 0 −3R2 + R3 → R3 0 −1 1 −1 0 0 2. (10 points) The augmented matrix of a linear system is given in row reduced form by 1 0 0 −2 5 . 0 1 −2 −3 2 Find the solution of the linear system. Solution: The system has infinitely many solutions. The free variables are x3 , x4 , the leading variables are x1 , x2 . The solution is x1 = 5 + 2t x2 = 2 + 2s + 3t x3 = s x4 = t. Page 2