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Unformatted text preview: MATH 265 FINAL EXAM, Spring 2007 Name and ID: Instructor: Section or class time: Instructions: Calculators are not allowed. There are 25 multiple choice problems worth 8 points each, for a total of 200 points. 1 14 2 15 3 16 4 17 5 18 6 19 7 20 8 21 9 22 10 23 11 24 12 25 13 1 1. For what values of h and k the system A x = b has infinitely many solutions? A = 1 1 4 3 3 h 1 8 , b =  2 k . A. h 6 = 12 and k any number B. h = 12 and k any number C. h = 12 and k = 6 D. h = 11 and k = 6 E. h = 6 = 11 and k 6 = 6 2 2. The inverse of the matrix A = 1 1 2 1 1 1 is A 1 = a 1 / 3 1 / 3 2 / 3 b 1 / 3 2 / 3 1 / 3 c . What is a + b + c ? A. 0 B. 1 / 3 C. 2 / 3 D. 1 / 3 E. 2 / 3 3 3. Let A , B and C be invertible n n matrices. If A 1 B 1 = C 1 , then what is A ? A. A = CB 1 B. A = C 1 B 1 C. A = BC 1 D. A = B 1 C E. A = BC 4 4. If ( x 1 , x 2 , x 3 ) is the solution of the following system of equations x 1 + 3 x 2 + x 3 = 1 2 x 1 + 4 x 2 + 7 x 3 = 2 3 x 1 + 10 x 2 + 5 x 3 = 7 then x 2 = A. 29 / 9 B. 8 / 9 C. 59 / 9 D. 9 / 8 E. 20 / 9 5 5. Which of the following statements are true? (i). A linear system of four equations in three unknowns is always inconsistent (ii). A linear system with fewer equations in than unknowns must have in finitely many solutions (iii). If the system A x = b has a unique solution, then A must be a square matrix. A. all of them B. (i) and (ii) C. (ii) and (iii) D. (iii) only E. none of them 6 6. If 1 2 1 3 ( 1 0 3 1 a b + 1 1 ) =  11 1 what is a + b ? A. 13 B. 5 C. 1 D. 5 E. 13 7 7. What vector is represented by the following: O y / x (1 , 2) (4 , 3) 4 j j j j j j j j A....
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 Spring '08
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