LinAlgPracticeExam3Spr08

# LinAlgPracticeExam3Spr08 - Name:_ Linear Algebra Practice...

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Linear Algebra Practice Exam 3 Spring, 2008 1. Let A = PDP -1 and compute A 4 , where . 1/2 0 0 1 D , 5 3 - 3 - 2 P = = 2. Let the matrix A be (i) Find the characteristic equation of A. (ii) Solve the characteristic equation of A to find the eigenvalues of A. 3. Diagonalize the following matrix: 4. Find T(a +bt +ct 2 ) as an element of 2 P where T is the linear transformation from 2 P to 2 P whose matrix relative to the basis B = {1, t, t 2 } is 5. Suppose the n × n matrices A and B are similar. Prove that: (i) det A = det B. (ii) A 2 and B 2 are similar. 6. Find an invertible matrix P and a matrix C of the form - a b b a such that the given matrix A satisfies A=PCP -1 , where = 3 1 2 - 5 A . . 2 7 6 0 1 0 3 2 5 - - . 3 4 1 0 5 0 0 0 5 A - = . 7

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## This note was uploaded on 04/29/2008 for the course MATH 3305 taught by Professor Engquist during the Spring '08 term at St. Edwards.

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LinAlgPracticeExam3Spr08 - Name:_ Linear Algebra Practice...

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