There is a linear transformation from P1 to P1

[Axoren]

Homework Statement

There is a linear transformation T from P1 to P1 where P1 is the set of all polynomials of degree at least 1.
T(1 + 2x) = 2 + 4x and T(4 + 7x) = -2 + 2x

Find T(-3 - 5x).

Homework Equations

T(1 + 2x) = 2 + 4x
T(4 + 7x) = -2 + 2x

The Attempt at a Solution

Basis B1 = [1, 2] [4, 7]
Basis B2 = [2, 4] [-2, 2]

[-3, -5] in terms of Basis 1 = [1, -1], bring that into Basis 1 gives you 1*[2, 4x] + -1*[-2, 2x] = [0, 6x]

The answer is not 6x.

 

[Dick]

Why do you think 1*[2, 4x] + -1*[-2, 2x] = [0, 6x]? That doesn't look at all right.

 

[Axoren]

Why do you think 1*[2, 4x] + -1*[-2, 2x] = [0, 6x]? That doesn't look at all right.

Haven't slept in 3 days, the other day, I was trying to calculate the cross product of two vectors in R5. What's worse, is I ended up with an answer.


Close this, the answer's 4 + 2x.