How can I find [L] from basis B to basis C, if basis B = {1 + x + x^2, 1 + x, 2x + x^2} and basis C = {1 + x, x - x^2, 3 + x^2}? L(p) = p + p', meaning that the linear transformation is the up to 2nd degree polynomial plus its own derivative.

The matrices A₁ = A3 [] = ^--^- A₂ = [] =[] A4 form a basis for the linear space V = R 2x2. Write the matrix of the linear transformation T: R 2x2R 2x2 such that T(A) = 3A + 10AT relative to this basis.

Suppose T: M2,2→→P2 is a linear transformation whose action on a basis for M2,2 is as follows: [18]-- Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. = -2x+5 T = 0 1 1 -2 -2 = -x+4 T -4 -2 = 2x² +4x-26 T 00 = -2x²+2x+10

Let L be a linear transformation on R2 such that L([1,1]) = ([-2,1]) and L([-1,1]) = [7,-1]. then what's the vector L([7,-1])   sorry to but the numbers in the brackets are in columns, I don't know how to write it thats why.