(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A = E4 in R4 (standard basis) and B = {x^2, x, 1} in P2 over R. If T is the linear transformation that is represented by

[tex]

\begin{bmatrix}1 & 1 & 0 & 1\\0 & 0 & 1 & -1\\1 & 1 & 0 & 1 \end{bmatrix}

[/tex]

relative to A and B, find the matrix that represents T with respect to A' and B' where

A' = {(1,0,0,0), (0,0,1,0), (1,-1,0,0), (0,-1,1,1)}

B' = {x^2 + 1, x, 1}

2. Relevant equations

3. The attempt at a solution

So by looking at this matrix T, it's clear that its a transformation from A to B, so we want the transformation matrix [tex]T_{B'A'}[/tex],

which is: [tex]T_{B'A'} = I_{B'B}T_{BA}I_{AA'}[/tex]

So I need to find [tex]I_{AA'}[/tex] and [tex] I_{B'B}[/tex].

For [tex]I_{AA'}[/tex], I write A' wrt A(which is standard basis of R4):

I get : [tex]I_{AA'} = \begin{bmatrix}1 & 0 & 1 & 0 \\0 & 0 & -1 &-1\\0 & 1 & 0 &1\\ 0&0&0&1 \end{bmatrix} [/tex]

Then for [tex] I_{B'B}[/tex], I write B wrt B', and get

[tex]I_{B'B} = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0\\-1 & 0 & 1 \end{bmatrix} [/tex]

Now I put them together to get something with lots of zeros.. which doesn't seem right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra - Change of basis question

**Physics Forums | Science Articles, Homework Help, Discussion**