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PirateFan308
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Homework Statement
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+x2, x}
Homework 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]
The Attempt at a Solution
So because the degree can be at most 2, the polynomials will be of the form a+bx+cx2. This can be denoted using a(1+x)+c(x+x2)+(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+x2+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.