sample_tt1_2

# 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 ² and B = - 21 11 0 - 1 . Calculate AB . e) Let S = { ±v 1 ,±v 2 3 } be a set of vectors in R 3 . State the deFnition of the set S being linearly independent. f) Explain why × ( ± 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 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 RRE± using elementary row operations. b) What is the rank of the coe²cient matrix?

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## This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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

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