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Unformatted text preview: Math 136 Sample Term Test 1  2 NOTES:  Questions 7, 10b on this test cover material that will not be covered on our term test 1. 1. Short Answer Problems a) List the 3 elementary row operations. b) What can you say about the consistency and the number of parameters (free variables) in the general solution of a system of 5 linear equations in 4 variables. c) What is the area of the parallelogram induced by ~a = (1 , 2) and ~ b = (4 , 9). d) Let A = 3 2 1 2 1 4 and B =  2 1 1 1 1 . Calculate AB . e) Let S = { ~v 1 ,~v 2 ,~v 3 } be a set of vectors in R 3 . State the definition of the set S being linearly independent. f) Explain why ~a ( ~ b ~ c ) must be a vector in the plane with vector equation ~x = s ~ b + t~ c , s,t R . 2. Consider the system of linear equations: 2 x + 3 y + 3 z = 9 3 x 4 y + z = 5 5 x + 7 y + 2 z = 14 a) Write the augmented matrix and row reduce it to RREF using elementary row operations....
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This note was uploaded on 01/18/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Math, Linear Algebra, Algebra

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