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Unformatted text preview: Newberger Math 247 Sample Exam 1 name: 1. The augmented matrix of a linear system is 2 1 8 1 2 4 2 1 1 1 2 . a. (9 points) Reduce the augmented matrix to reduced echelon form. 2 1 8 1 2 4 2 1 1 1 2 ∼ 1 1 1 2 1 2 1 2 1 8 1 ∼ 1 1 1 2 1 2 1 3 6 3 ∼ 1 0 3 1 0 1 2 1 0 0 b. (9 points) Write the general solution of the linear system in parametric vector form. The solution is x 1 3 x 3 = 1 x 2 + 2 x 3 = 1 x 3 is free. In parametric form, we have x 1 x 2 x 3 = 1 + 3 x 3 1 2 x 3 x 3 = 1 1 + 3 2 1 x 3 , where x 3 is any real number. c. (5 points) Give a geometric description of the solution set. This is the line through 1 1 parallel to 3 2 1 . 1 2. Let a 1 = 1 5 9 , a 2 = 2 6 10 , b = 4 8 12 . a. (6 points) Is b is in Span { a 1 , a 2 } ? Explain. We need to determine whether or not the system [ a 1 , a 2 ] x = b has a solu tion. The augmented matrix for this system is 1 2 4 5 6 8 9 10 12 ∼ 1 2 4 4 12 8 24 ∼ 1 2 4 0 1 3 0 0 0...
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This note was uploaded on 01/12/2010 for the course MATH 247 taught by Professor F,newberger during the Spring '03 term at Stanford.
 Spring '03
 F,newberger
 Math

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