Let L be the line in R³ spanned by the vector Let A be the linear transformation given by rotating 180° rotation around the axis L. What are the eigenvalues of A? Justify your answer.

Solve the question below:

Consider the linear transformation T: R^ →R" whose matrix A relative to the standard basis is given. [³ A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (1₁, 12) = 4,5 B₂ 3-2 (b) Find a basis for each of the corresponding eigenspaces. B₁ = 1,2 128 1,1 = A' = 1 6 (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). X 5 5 1 2 ↓ 1

Please help me the first 3 parts. Part A part B and part C. Please make sure type by computer although

Consider the vector space V of all the real polynomials of degree less than or equal to three,  p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.

What is the vector where it is orthogonal to the eigenvectors