1. ## Linear algebra problem

Can someone show me how to do this problem? I really have no clue.
Given the vector space V of all the polynomials of degree less than or equal to 2. Consider the linear transformation $L: V \rightarrow V$ by $L= c^2+c+I$. For example, $L(x^2)=x^2+2x+2$. Compute det(L) and Tr(L).
I think I have to pick a basis in this vector space, so I can pick the standard basis, but I have no clue how to proceed.

2. Originally Posted by jackie
Can someone show me how to do this problem? I really have no clue.
Given the vector space V of all the polynomials of degree less than or equal to 2. Consider the linear transformation $L: V \rightarrow V$ by $L= c^2+c+I$. For example, $L(x^2)=x^2+2x+2$. Compute det(L) and Tr(L).
I think I have to pick a basis in this vector space, so I can pick the standard basis, but I have no clue how to proceed.
The definition of $L$ is not clear.

3. Originally Posted by ThePerfectHacker
The definition of $L$ is not clear.
I copied the problem from my problem set. I am so confused.