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) State the definition of the rank of a matrix. 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) Let A = ± 3 2 1 - 2 1 4 ² and B = - 2 1 1 1 0 - 1 . Calculate AB . d) 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. e) Give an example of vectors ~u and ~v in R 3 such that the vector equation ~x = s~u + t~v , s,t R , is not a plane. 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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sample_tt1_2 - Math 136 Sample Term Test 1 - 2 NOTES: -...

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