Linear algebra problem

**jackie** · February 6th 2009, 12:54 PM

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.

**ThePerfectHacker** · February 6th 2009, 07:38 PM

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.

**jackie** · February 6th 2009, 11:49 PM

Originally Posted by ThePerfectHacker

The definition of $L$ is not clear.

I copied the problem from my problem set. I am so confused.

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