The matrix A below has charachteristic polynomial (λ+1)2(λ-2)2. Compute bases for the(+2)eigenspace and the (-1)eigenspace and explain why A is not diagonalizablehttp://www.cramster.com/Answer-Board...9312505233.gif

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- April 11th 2008, 07:46 AMmatty888Matrix basesThe matrix A below has charachteristic polynomial (λ+1)2(λ-2)2. Compute bases for the(+2)eigenspace and the (-1)eigenspace and explain why A is not diagonalizablehttp://www.cramster.com/Answer-Board...9312505233.gif
- April 11th 2008, 12:21 PMMoo
Hello,

As in your previous thread, solve for X in :

(definition of eigenvalue, that will give you eigenspaces for each eigenvalues)

So solve for X in -> (+2) eigenspace

-> (-1) eigenspace

If the dimension of the (+2) eigenspace plus the dimension of the (-1) eigenspace is inferior to 4, then the matrix is not diagonalizable.