A is a 4x4 matrix with exactly the eigenvalues 2 and 7, andcorresponding eigensp

Question

A is a 4x4 matrix with exactly the eigenvalues 2 and 7, andcorresponding eigenspaces V and W. If possible, find thecharacteristic polynomial. (a) dim V =3 (b) A is diagonalizable and dim W=2
I think (a) is -(t-2)^3 (t-7) (b) is -(t-2)^2 (t-7)^2 but I'm not even sure if there is sufficent information or ifA is diagonalizable is adding necessary information.

Help is appreciated. (a) dim V =3 (b) A is diagonalizable and dim W=2
I think (a) is -(t-2)^3 (t-7) (b) is -(t-2)^2 (t-7)^2 but I'm not even sure if there is sufficent information or ifA is diagonalizable is adding necessary information.

Help is appreciated.
Help is appreciated.

Explanation / Answer

A is a 4x4 matrix with exactly the eigenvalues 2 and 7, andcorresponding eigensp

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