Quote:

Originally Posted by

**Dranalion** Consider the linear transformation T : P2 -> P1 specified by T(a0 + a1x +

a2x^2) = (-3a0 + 14a1 - 6a2) + (a0 - 4a1 + 2a2)x.

Have you **tried** anything yourself? You shouldn't ask others to help until you have tried yourself and then you should show what you have tried.

Quote:

(a) Write this an equivalent mapping from R^3 to R^2.

$\displaystyle a_0+ a_1x+ a_2x^2$ is associated with $\displaystyle (a_0, a_1, a_2)$ and $\displaystyle b_0+ b_1x$ with $\displaystyle (b_0, b_1)$. $\displaystyle (a_0, a_1, a_2)$ is mapped to $\displaystyle (-3a_0+ 14a_1- 6a_2, a_0- 4a_1+ 2a_2)$

Quote:

(b) Using your answer to (a) or otherwise, specify the standard matrix

representation of T.

There are several **different** ways to do this. I don't know which you have been taught. The simplest is to apply the transformation to (1, 0, 0), (0, 1, 0), and (0, 0, 1) in turn. The results will be the three columns of the matrix.

[quote](c) The set D = {-3 + x; 7 - 2x} is also a basis for P1. Write down the

transition matrix PS;D, where S1 is the standard basis for P1, and use

it to calculate the transition matrix PD;S.[quote]

The transition matrix changes each vector v, written as (a, b) with v= a+ bx, in the standard basis, into (p, q) where v= p(-3+x)+ v(7- 2x). Find what (a, b) is changed into and that will give the columns for the transition matrix.

Quote:

(d) Calculate the matrix [T]D;S2.

This is now just matrix multiplication.

Quote:

Any help is much appreciated,

Dranalion