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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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 Spring '10
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