In each case, compute the characteristic polynomial cT(x). (a) T : R2 R2, T(a, b) =

Question:

In each case, compute the characteristic polynomial cT(x).
(a) T : R2 †’ R2, T(a, b) = (a - b, 2b - a)
(b) T: R2 †’ R2, T(a, b) = (3a + 5b, 2a + 3b)
(c) T: P2 †’ P2, T(a + bx + cx2) = (a - 2c)
+ (2a + b + c)x + (c - a).x2
(d) T: P2 †’ P2, T(a + bx + cx2) = {a + b - 2e)
+ (a- 2b + r)x + {b - 2a)x2
(e) T: R3 †’ R3, T(a, b, c) = (b, c, a)
(f)