math34600fall2005 - Math 34600 Final Exam Fall 2005...

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Math 34600 Final Exam Fall 2005 Instructions: Answer any seven questions. Omit one. 1a) Find the inverse of the matrix . 11 0 12 1 01 2 A   =−  b) Using solve the system of equations: . 1 A 1 22 xy z yz −= −+ − = −+ =− 2a) Let . Find . 02 1 1 10 10 01 0 1 23 0 3 B = det( ) B b) Find det( . c) Find det(3 . 2 ) B ) B 3a) Find all solutions of the system . 0 42 52 xyz z xy z ++= −+ −= −+− = 3 3 } 2 b) Explain why you cannot use Cramer's Rule to answer problem 3a). 4) Find all eigenvalues and all associated eigenvectors for the matrix . 12 21 A = 5) Let . Which of the following subsets is a subspace of ? { 2 quadratic polynomials = 2 P a) {quadratic polynomials with }. () px (0) 1 p = b) {quadratic polynomials with }. ( ) (1) 0 p = c) For each of the subsets that are subspaces, find a basis for the subspace. 6) Prove or disprove the following statements about matrices A and B . nn × a) If A and B are invertible, so is . AB b) If A and B are invertible, so is . AB + c) If λ is an eigenvalue for A , then is an eigenvalue for
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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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math34600fall2005 - Math 34600 Final Exam Fall 2005...

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