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Linear Algebra-Homework 13 March 29, 2012 Problem 1 Find the eigenvalues and eigenvectors of the following linear transformations and decide if the...

Can you solve problem 2 part 1?

Linear Algebra-Homework 13 March 29, 2012 Problem 1 Find the eigenvalues and eigenvectors of the following linear transformations and decide if the transformations are diagonalizable. 1. T ( f ) = f 0 - f from C to C 2. T ( f ) = 3 f 0 - 5 f from C to C 3. L ( A ) = A + A T from M 2 ( R ) to M 2 ( R ) 4. T ( f ) = f 0 from P 2 ( R ) to P 2 ( R ) . 5. T ( f ( x )) = f (2 x ) from P 2 ( R ) to P 2 ( R ) . 6. T ( f ( x )) = f (3 x - 1) from P 2 ( R ) to P 2 ( R ) . Problem 2 Find the eigenvalues and eigenvectors of the following matrices and decide if they are diagonalizable. 1. ± 1 2 3 6 ² 2. ± 1 4 1 - 2 ² 3. 3 - 4 0 2 - 3 0 0 0 1 4. 1 1 1 1 1 1 1 1 1 5. 4 0 - 2 0 1 0 1 0 1 6. 1 1 1 0 1 0 0 1 0 Problem 3 For what values of a , b and c are the following matrices diagonalizable ? 1. ± a b b c ² 1
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2. ± 1 1 a 1 ² 3. 1 a b 0 2 c 0 0 1 4. 1 a b 0 1 c 0 0 1 2
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