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Unformatted text preview: MA 265 GOINS SAMPLE 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 three equations can have exactly three solutions. A. True B. False 2. Homogeneous linear systems are always consistent. A. True B. False 3. The following systems of linear equa tions are equivalent: x + y = 3 2 x + y = 4 x + 3 y = 4 3 x 2 y = 1 A. True B. False 1.2: Matrices 4. Consider the following 2 2 matrix: A = bracketleftbigg 1 2 3 4 bracketrightbigg . What is the (2 , 1)entry? A. 2 B. 3 C. 4 D. None of the above 5. Consider the matrices A = bracketleftbigg 1 1 0 1 bracketrightbigg and B = bracketleftbigg 1 0 0 1 bracketrightbigg . Which of the following is a linear combina tion of A and B ? i. bracketleftbigg 3 0 0 2 bracketrightbigg ii. bracketleftbigg 1 0 1 1 bracketrightbigg iii. bracketleftbigg 2 1 0 2 bracketrightbigg A. (iii) only B. (i) and (iii) C. (i), (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 3 vectors u = r 4 5 and v = 3 2 1 . For what value of r do we have u v = 0? A. 1 B. 0 C. 2 D. None of the above 7. Let u and v be 3vectors such that u v = 1. What is the dot product of 2 u with 3 v ? A. 1 B. 5 C. 6 D. Cannot be determined 8. If A is an n n matrix such that A 2 = A , then A = I n must be the identity matrix....
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This note was uploaded on 02/25/2010 for the course MA 00265 taught by Professor ... during the Spring '10 term at Purdue University Calumet.
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