Question: 4 . Suppose T: RS - R with T ( x) = Ax is a linear transformation such that ( a) (o. 0, 0 ,

4 . Suppose T: RS -" R with T ( x) = Ax is a linear transformation such that ( a) (o. 0, 0 , 1 . ( ) and Co. 0 . 0 , 1 . 1) lie in the kernel of T, and " b) All vectors of the form ( X, . X x, .0. 0 ) are reflected about the plane X, tx, fx = = 0 ( 1 ). compute all the eigenvalues of A and a bas's of each eigenspace (2) . Is A diagnosizable? If yes, write down it's diagonalization ( you can leave it as a product of matrices ). If no, why not? ( no need to compute the inverse of P )

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