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Unformatted text preview: then dividing the third column by 2. 4. 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 . 5. Compute the inverse of the matrix A = 1 1 1 23 1 1 3 . ( Use any method you like.) 6. Calculate the following determinant. det 1 1 1 1 1 2 1 1 1 1 4 1 1 1 1 3 7. Find the eigenvalues and eigenvectors of the matrix A = ± 1 0 1 1 ² . Is A diagonalizable? 2 8. (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....
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 Spring '10
 DONALDSON,NEIL
 Linear Algebra, Matrices

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