# Question regard writing linear transformation into matrix

• October 5th 2013, 08:12 PM
junkwisch
Question regard writing linear transformation into matrix
Hey guy, I have some problem regard to linear transformation, I can conver something like this $T(x, y, z)=(x+ 2*y -z, x-y+2z,-y+z)$ into matrix form but I don't know how to convert "the following" into matrix form. Can you guy give me advice about how to do it?

Let $T : P3 --> P3$be the linear transformation deﬁned by
$T(p(x)) = p(x+ 1) +p(2-x)$
(For example, $T(x^2 + 7) = (x+ 1)^2 + 7 + (2-x)^2 +7=2x^2-4x+ 18.)$

Find the matrix of T with respect to the standard basis $B = {1, x, x^2, x^3}$ for P3.

best regard
Junks
• October 6th 2013, 07:50 AM
emakarov
Re: Question regard writing linear transformation into matrix
Start by writing out explicitly the value of T on an arbitrary cubic polynomial ax³ + bx² + cx + d.