midterm_1_exam - MA 265 GOINS MIDTERM EXAMINATION#1...

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Unformatted text preview: MA 265 GOINS MIDTERM EXAMINATION #1 Instructions: Circle the correct answer on the follow- ing pages. You have 50 minutes to com- plete 35 problems. No textbooks, personal notes, calculators, or computing aids are allowed during the examination period. Each problem is worth 3 points. This examination is worth 105 points. Name: 1 2 MA 265 MIDTERM #1 Chapter 1. Linear Equations and Matrices 1.1: Systems of Linear Equations 1. A linear system of two equations can have exactly two solutions. A. True B. False 2. The following system of linear equations is consistent: x + y = 0 2 x + 3 y = 0 A. True B. False 3. The following systems of linear equa- tions are equivalent: x + y = 2 2 x + y = 3 x + 3 y = 4 3 x 2 y = 1 A. True B. False 1.2: Matrices 4. Consider the following 3 3 matrix: A = 1 2 3 4 5 6 7 8 9 . What is the (2 , 3)-entry? A. 5 B. 6 C. 8 D. None of the above 5. Consider the matrices A = bracketleftbigg 1 2 bracketrightbigg and B = bracketleftbig 3 4 bracketrightbig . Which of the following operations is de- fined? i. A + 2 B ii. A B T iii. 3 A T + B A. (i) only B. (iii) only C. (ii) and (iii) D. None of the above MA 265 MIDTERM #1 3 1.3: Matrix Multiplication 6. For a real number r , consider the 2- vector x = bracketleftbigg r 4 bracketrightbigg . For which values r do we have x x = 25? i. r = 3 ii. r = 0 iii. r = 3 A. (i) only B. (i) and (ii) C. (i), (ii), and (iii) D. None of the above 7. Let A be an m n matrix. Then A T A is defined. A. True B. False 8. Consider the 2 2 matrices A = bracketleftbigg 0 1 0 0 bracketrightbigg and B = bracketleftbigg 0 0 1 0 bracketrightbigg . Which of the following matrix products is the zero matrix?...
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midterm_1_exam - MA 265 GOINS MIDTERM EXAMINATION#1...

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