Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. -{[: :] [}]- [ :]} «-{{; :]- [; :] [: :} {[: ]. 1 0 3 0 0 1 1 1 3 1 3 0 0 В B' 2 3 4...

Extracted text: Consider the following bases B and B' for some subspace of M2x2(R), the vector space of all 2 by 2 matrices over R. -{[: :] [}]- [ :]} «-{{; :]- [; :] [: :} {[: ]. 1 0 3 0 0 1 1 1 3 1 3 0 0 В B' 2 3 4 3 2 1 0 -8 3 4 -6 -1 (a) Find the coordinate matrix of A = 4 relative to the basis B', that is 6. [x(A)]g". (b) Calculate the transition matrix PB→B. [Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).