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Unformatted text preview: Problem 1 2 3 4 5 Bonus: Total: Points 15 13 12 5 5 10 50+10 Scores Mat 310 Linear Algebra Fall 2004 Name: Id. #: Lecture #: Test 1 (September 24 / 50 minutes) There are 5 problems worth 50 points total and a bonus problem worth up to 10 points. Show all work. Always indicate carefully what you are doing in each step; otherwise it may not be possible to give you appropriate partial credit. 1. [15 points] Consider the homogeneous system of linear equations x 1 + x 2 + 2 x 3 2 x 4 = 0 x 1 5 x 2 x 3 + 7 x 4 = 0 x 1 x 2 + x 3 + x 4 = 0 (a) [3 points] Write down the matrices A , X , and O for which the system is in matrix form AX = O . Solution: A = 1 1 2 2 1 5 1 7 1 1 1 1 , X = x 1 x 2 x 3 x 4 , O = (b) [6 points] Using the GaussJordan algorithm, compute the rowreduced echelon matrix R which is row equivalent to A . Solution: A R 2 R 2 R 1 1 1 2 2 6 3 9 1 1 1 1 R 3 R 3 R 1 1 1 2 2 6 3 9 2 1 3 R 3 R 3 1 3 R 2 1 1 2 2 6 3 9 R 2  1 6 R 2...
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 Spring '10
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