(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?

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# Linear Algebra - Change of basis question

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