Define a linear T: R₂[x] → R3 [x] by T(p(x)) = x²p"(x) − 2p'(x) + xp(x), where p'(x) and p''(x) are the first and second derivatives of the polynomial p(x), respectively. Determine the matrix of T relative to the standard basis of R₂ [x] and R3[x].

Use matrices to solve the equations: 2х + Зу %3D11 -3x - 4y = -13 .a X = 1 and y .b X = -2 and y = 5 %D .C x = 5 and y = -7 .d X = -5 and y = 7

please add more information. I need the step by step process as I do not understand where the polynomial equation was derived and how the answers for lamda were derived. and what is done with the matrixes. How D is derived. Please provide each step with english explanation with what each step is and why it is being done. Thank you

must solve all parts for upvote