sample_tt1_1

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

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Math 136 Sample Term Test 1 - 1 NOTES: - Questions 4d, 5, 6 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) 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) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ? d) 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: 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 coefficient matrix? c) Find the general solution of the system. 3.
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This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

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

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