Linear transformation

[daniele002]

Hey! I need help with this linear trasformation. I have to find the associated matrix but I have no idea how to do that.
I have tried writing down p(x+1) as a₀+a₁(x+1)+a₂(x+1)² and I got
f(1)=(1,0,0)
f(x)=(1,1,0)
f(x²)=(1,2,1)
but this is wrong. Any suggestions? Thank you in advance

 

[Steven G]

Please state the entire problem.

 

[daniele002]

I need to find the associated matrix of that linear transformation. The basis to use are the two columns on the right

 

[Steven G]

OK, I understand now. So where are you stuck? What have you tried?

 

[daniele002]

I think I have a problem when it comes to use the second basis. I know how to do it for numbers but not for polynomials.