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## Homework Statement

The Question:

The map is given: [tex]L\rightarrow \Re_{2} \rightarrow \Re_{3}, p \rightarrow[/tex] p' + q*p , with q(x) = x.

Now i should find the representing matrix for L with respect to the bases {1+x, x+x

^{2}, 1+x

^{2}} for [tex] \Re_{2}[/tex] and {1,x,x+x

^{2},1+x

^{3}} for [tex] \Re_{3}[/tex].

## The Attempt at a Solution

I dont know what i should do here ^^. But i tried to calculate it.

p is the polynomial, so i thought its like this:

p = a

_{0}(1+x) + a

_{2}(x+x^2) + a

_{3}(1+x^2)

So i can calculate [tex]p\rightarrow p' +q*p:[/tex]

[tex]p\rightarrow a_{0}+a_{1} + 3a_{1}x + a_{0}x + 2a_{2}x^2 + 2a_{1}x^2 + 2a_{2}x^3[/tex]

Then i just counted the coressponding values together, means

a

_{0}~ 1+x --> 1 + 1 + 0 + 0

a

_{1}~ x+x

^{2}--> 1 + 3 + 2 + 0

a

_{2}~ 1+x

^{2}--> 0 + 0 + 2 + 2

Puting this all together gives the repr. Matrix

| 1 1 0 |

| 1 3 0 |

| 0 2 2 |

| 0 0 2 |

Is this somehow correct or completely wrong? ^^

I'm missing the second base here..

Does anyone knows a good website (linear algebra 1) ? I have exam in little more than week and still a lot to learn.

Thx

Mumba