sol_310f04_1 - Problem 1 2 3 4 5 Bonus: Total: Points 15 13...

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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 Gauss-Jordan algorithm, compute the row-reduced 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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sol_310f04_1 - Problem 1 2 3 4 5 Bonus: Total: Points 15 13...

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