(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V be polynomials, with real coefficients, of degree at most 2. Suppose that [itex]T:V→V[/itex] is differentiation. Find the [itex]B[/itex]-matrix [T]_{B}if B is the basis of V

B = {1+x, x+x^{2}, x}

2. Relevant equations

For [itex]T:V→V[/itex] the domain and range are the same

[T]_{B}is the matrix whose i-th column is [itex][T(vi)]_B[/itex]

[itex][T(v)]_C = A[v]_B[/itex] where [itex]A=[T]_B[/itex]

3. The attempt at a solution

So because the degree can be at most 2, the polynomials will be of the form a+bx+cx^{2}. This can be denoted using a(1+x)+c(x+x^{2})+(b-a-c)(x). It will turn into a+bx (because we take the derivative, we take powers to a max of 1) and we would say a(1+x)+0(x+x^{2}+b(x). After this, I'm not sure how to find the B-matrix, as I'm a bit confused as to what it is exactly.

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# Linear Transformation: B-matrix [T]B

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