math34600fall2006 - Math 34600 Final Exam, Fall 2006 1....

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Math 34600 Final Exam, Fall 2006 1. Invert the following matrices, if possible. (a) (5 points) A = ± 2 - 3 - 2 4 ² (b) (5 points) A = ± 4 - 8 1 - 2 ² 2. Let A = 2 6 6 2 7 6 2 7 7 . (a) Compute A - 1 , if possible. (5 points) (b) Find the rank and nullity of A . (5 points) (c) Find all solutions of Ax = 1 2 3 . (5 points) 3. Let A = 0 1 7 8 1 3 3 8 - 2 - 5 1 - 8 . (a) Find all solutions of Ax = - 13 - 28 43 . (5 points) (b) Find a basis of N ( A ). (5 points) (c) Find the rank and nullity of A . (5 points) 4. Let A = 2 1 3 1 1 0 1 1 0 2 1 0 0 1 2 3 . 1
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(a) Compute det A . (5 points) (b) Is A invertible? Is A surjective? Why or why not? (5 points) 5. Let A = ± 8 - 10 3 - 3 ² . (a) Find the eigenvalues of
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This note was uploaded on 01/29/2012 for the course MATH 203 taught by Professor Snell during the Spring '11 term at City College of San Francisco.

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math34600fall2006 - Math 34600 Final Exam, Fall 2006 1....

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