# Homework problem

Consider the basis {1, x,(x − 1)^2} for P2 and let F : P2 → P2 be a linear transformation.

Let F(1) = (x + 1)^2, F(x) = x, F((x-1))^2.

Find the rule for F(a x^2 + b x + c).

Homework problem

asked
**
2015-11-08 17:57:28 -0600
**

This post is a wiki. Anyone with karma >750 is welcome to improve it.

Consider the basis {1, x,(x − 1)^2} for P2 and let F : P2 → P2 be a linear transformation.

Let F(1) = (x + 1)^2, F(x) = x, F((x-1))^2.

Find the rule for F(a x^2 + b x + c).

Asked: **
2015-11-08 17:57:28 -0600
**

Seen: **256 times**

Last updated: **Nov 09 '15**

multivariable division algorithm

How can I sketch the graph in sagemath like picture?

Find and plot the Fourier transform of the Ricker wavelet

pseudoprime numbers solve in sage [closed]

Plotting Fermat' s Spiral, which requires polar coordinates, r=2theta

Is there a more elegant way to make an interactive worksheet for students?

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

You should at least make

someefforts to make your question intelligible!This looks like homework. If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.

More precisely, this question doesn't look like it it related to Sage!

I guess P2 is the vector space of polynomials of degree less or equal two. Then we get a map F on the system 1, x, (x-1)^2 with values in the same space, which we extend linearly. Unfortunately the map is defined only on the first two elements, for the third one we run into human compiler error.