For each linear operator T on V, find the eigenvalues of T and an ordered basis ofV such that [T] is a diagonal matrix.

V=R3 T(a, b, c ) = (7a-4b+10c, 4a-3b+8c, -2+b-2c)

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I am not sure what I am doing

I have gotten [T]where = {(1,0, 0) (0, 1, 0) (0, 0, 1)} to be:

| 7 -4 -10|

|-4 -3 8|

|-2 -1 -2|

det([T] - t I₃) = -t³+9t²- 41t -38

but this charpoly is not correct because book says that the t= -1, 1, 2

please explain what I have done wrong so far and give me a guidelineon how to finish this problem.