For each of the following linear operators T on a vector space V and ordered bases 0

QUESTION:

For each of the following linear operators T on a vector space V and ordered bases 0, compute [T]/?, and determine whether 0 is a basis consisting of eigenvectors of T. (a) V = R2 , T 10a - 66 17a - 106 , and 0 = (b) V = Pi (R), J(a + 6x) = (6a - 66) + (12a - 116)x, and 3 = {3 + 4x, 2 + 3x} (c) V = R 3a + 26 - 2c' - 4 a - 36 + 2c . and (d) V = P2 (i?),T(a + 6x + cx2 ) = (-4a + 26 - 2c) - (7a + 36 + 7c)x + (7a + 6 + 5c>2 , and 0 = {x - x 2 , - 1 + x 2 , - 1 - x + x 2 }