Question: Let T L(R 3 ) be given by T(a, b, c) = (b + c, 2b, 2a + b + 3c). You can assume as

Let T L(R 3 ) be given by T(a, b, c) = (b + c, 2b, 2a + b + 3c). You can assume as given the fact that the eigenvalues of T are 1 and 2.

(a) Find a basis of the eigenspace for each eigenvalue of T.

(b) Determine whether T is diagonalizable.

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