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sample_tt1_2 - Math 136 Sample Term Test 1 2 NOTES...

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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 0 - 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. b) What is the rank of the coefficient matrix? c) Find the general solution of the system.
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