4. Let V = P2(R) and suppose that T : V ? V is a linear mapping whose matrix representation in the standard basis of V is given by M(T) = ? 1 0 -1 ? ? 0 2 2 ? ? 1 1 0 ? a. Find the polynomial Tp if p(x) = 7 - x + 2x^2. b. Find q(x) if (Tq)(x) = 4x + 2x^2. c. Find a basis for null(T). (Note: Your basis should not consist of vectors in R^3.)
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We need to find Tp if p(z) = 7 - x + 2x^2. To do this, we can represent p(z) as a vector in the standard basis of V: p = \begin{bmatrix} 7 \\ -1 \\ 2 \end{bmatrix} Now, we can find Tp by multiplying M(T) by p: Tp = M(T)p = \begin{bmatrix} 0 & 2 & 2 \\ 1 & 0 & 0 Show more…
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