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Unformatted text preview: then dividing the third column by 2. 4. Let A be a 5 5 matrix such that A =A t . Compute det( A ). 5. Solve the following system of equations. ( Use any method you like.) x 1 + 2 x 24 x 3 = 0 , 3 x 1 + x 2 + 4 x 3 = 21 , 2 x 1 + 4 x 26 x 3 = 2 . 6. Compute the inverse of the matrix A = 1 1 1 23 1 1 3 . ( Use any method you like.) 7. Calculate the following determinant. det 1 1 1 1 1 2 1 1 1 1 4 1 1 1 1 3 8. Find the eigenvalues and eigenvectors of the matrix A = 1 0 1 1 . Is A diagonalizable? 2 9. (a) Calculate the eigenvalues of the matrix A = 1 0 1 0 2 0 1 0 1 . (b) Find all eigenvectors of A . (c) Find an invertible matrix S and a diagonal matrix D such that S1 AS = D. (d) Compute e A ....
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This note was uploaded on 03/11/2012 for the course MATH 2J 44360 taught by Professor Donaldson,neil during the Spring '10 term at UC Irvine.
 Spring '10
 DONALDSON,NEIL

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