Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1)...

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x, x2} for P2.

(a) Find the matrix A for T with respect to the basis B.

(b) Find the eigenvalues of A, and a basis for R 3 consisting of eigenvectors of A.

(c) Find a basis for P2 consisting of eigenvectors for T.

Expert Solution

milcah answered 2 years ago

Find the rank and the nullity of the linear transformation: T : P2 → P1, T(?...

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