midterm-1-solns

midterm-1-solns - Math 33A Spring 2008 First mid-term exam...

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Unformatted text preview: Math 33A Spring 2008 First mid-term 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 mid-term 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 Gauss-Jordan 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.

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midterm-1-solns - Math 33A Spring 2008 First mid-term exam...

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