sample_tt1_1

# sample_tt1_1 - Math 136 Sample Term Test 1 NOTES Questions...

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Math 136 Sample Term Test 1 NOTES: - Questions 4d, 5, 6 on this test cover material that will not be covered on our term test 1. - Students had 90 minutes to write this test, where you will have 110 minutes. 1. Short Answer Problems a) List the 3 elementary row operations. b) Does the spanning set span { (1 , 2 , 1) , (0 , 1 , 0) , (1 , 0 , 1) } represent a line or a plane in R 3 ? Give a vector equation which describes it. c) What is the area of the parallelogram induced by ±a = (2 , 3) and ± b = (1 , - 1). d) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ? e) 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: z 1 - z 2 + iz 3 =2 i (1 + i ) z 1 - iz 2 + iz 3 = - 2+ i (1 - i ) z 1 +( - 1+2 i ) z 2 + (1 + 2 i ) z 3 = 3 + 2 i a) Row reduce the matrix to RREF using elementary row operations. b) What is the rank of the coe±cient matrix? c) Find the general solution of the system. 3. Let S = 1 2 1 , - 1 3 2 , 2 4 - 1 . a) Determine if 1 1 1 is in the span of S . If so, write it as a linear combination of the vectors in S . b) Determine if S is linearly independent or dependent.

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sample_tt1_1 - Math 136 Sample Term Test 1 NOTES Questions...

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