MATH311 midterm1-ans

MATH311 midterm1-ans - Math 311 midterm exam I answers 1 We...

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Unformatted text preview: Math 311 midterm exam I answers 1. We need to solve the system t 1 1 1 - s - 1 1 = 1 1 1- 1 1 t s = 3 1 2 . Using row reduction, 1 1 4 1- 1 2 1 3 → 1 1 4- 2- 2- 1- 1 → 1 1 4 0 1 1 0 0 → 1 0 3 0 1 1 0 0 . Thus t = 3 , s = 1 is a solution. So the lines intersect, at the point t 1 1 1 = 1 - 1 1 + 3 1 2 = 3 3 3 . 2. The matrix form of this system of equations is 1- 1 1- 5 2- 2 2 1 1 . Using row reduction, we get 1- 1 1- 5 2- 4 12 1 1 → 1- 1 1- 5 1- 2 6 1 1 → 1- 1 1- 5 1- 2 6 3- 6 → 1- 1 1- 5 1- 2 6 1- 2 → 1- 1 0- 3 1 0 2 0 1- 2 → 1 0 0- 1 0 1 0 2 0 0 1- 2 , so that x =- 1 , y = 2 , z =- 2 ....
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MATH311 midterm1-ans - Math 311 midterm exam I answers 1 We...

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