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Unformatted text preview: Math 33A Spring 2008 First midterm exam Name: Student ID: Instructions. There are five problems, each of which is worth 10 points. Answer each question. For full credit, show all work. Books, electronic devices, and notes may not be used. A piece of scratch paper is attached to the end of the exam. Problem Score 1 2 3 4 5 Total First midterm exam 2 1. (10 points) Consider the following system of linear equations: y + 2 z = 1 2 x y 2 z = 7 x + y + 2 z = 5 . Perform GaussJordan elimination on this system. If the system has any solutions, find all of them, and describe the solution set geometrically. If the system has no solution, state this. Solution: We form the augmented matrix A = 1 2 1 2 1 2 7 1 1 2 5 , and then perform the following row operations: 1 2 1 2 1 2 7 1 1 2 5 I III = 1 1 2 5 2 1 2 7 1 2 1 II 2 I = 1 1 2 5 3 6 3 1 2 1 II  3 = 1 1 2 5 0 1 2 1 0 1 2 1 I II,III II = 1 0 0 4 0 1 2 1 0 0 0 0 So x = 4, y + 2 z = 1. For a real parameter t , we set the free variable...
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This note was uploaded on 05/01/2008 for the course MATH 33a taught by Professor Lee during the Spring '08 term at UCLA.
 Spring '08
 lee
 Math

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