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Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 −...

Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 − 3x2), v = (1, −1), and p(z) = z^2 − 3z + 2. Compute p(T), show that p(T)v = 0, and show that NOT all the roots of p(z) are eigenvalues of T.

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A function T is said to be linear transformation if it preserves the addition and sclar multiplication.

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