Question: Let R[t]2 be the vector space of polynomials with real coefficients of degrees less than or equal 2. 22 LetT:R[t]2 R[t]2 bealinearoperatordefinedbyT(a+bt+ct )=6a+(6c+b)t . (a)

Let R[t]2 be the vector space of polynomials with real coefficients of degrees less than or equal 2.

22 LetT:R[t]2 R[t]2 bealinearoperatordefinedbyT(a+bt+ct )=6a+(6c+b)t .

(a) Compute eigenvalues of T.

(b) Find bases for each of the eigenspaces of T .

(c) Determine whether T is diagonalizable or not.

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