1. Let B = {v1, v2, va} C IR3 where v. - 8 - - 6 - - (a) Verify that B is a basis of IR3. (b) Write v = -4v1 + 2v2 -3va with coordinates relative to the basis B. (c) What is the matrix that converts vectors with coordinates relative to the basis B into vectors with coordinates relative to the canonical (standard) basis? (d) What is the matrix that converts vectors with coordinates relative to the standard basis into vectors with coordinates relative to the basis B? Give this matrix in terms of C, and then determine what this matrix is. (e) Convert into a vector in standard coordinates. B (f) Convert into a vector with coordinates relative to the basis B. (g) Suppose that 7': IR -> R" which satisfies T(v1) = -v2, T(v2) = -V3, T(v3) = -VI. Determine the matrix B which represents the transformation T' using coordinates relative to the basis B and then determine if the matrix B is diagonalizable. (h) Determine the matrix A which represents the transformation 7 using coordinates relative to the standard basis. (i) Compute B3. (j) Compute A3 and A3000 without a calculator