Background: 1. 2. Consider the linear map D: P2(R) + P1(R) defined by D(a + bx...

Question

Question

Background:

Consider the linear map D: P2(R) + P1(R) defined by D(a + bx + cx?) = (a + bx + cx?) = 6+2cx, dr and the linear map T : P1(R)

1.

We know from Calculus (a+bt)dt = a+bx. Compute [D] [T]& and verify this. 2.

Compute (T]*[D] . Is the composite map T o D invertible? Explain your answer.

Answer 1

Answer #1

(A) d calculation - 2 O 0-1+ O 9(x-) 0-1tax P(x)= 2 O.t1 +O. TO 1 0140. x T lx) ITTH O So 2. 0 1 fo cleany T since not invert

Answer 2

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