{MU

denote the standard basis for R³.

(a) Find the change of coordinates matrix 5Pg.

6. Let B=

be a basis for R³ and let S =

-{8-0-8}

(b) Find the change of coordinates matrix Ps.

(c) Find the product of two matrices you obtained in part a) and part b), namely

calculate the product BPs sPg. Is the result surprising? Why and why not?

(d) Use one of the matrices you found in part a) or part b) to find [v] if =

2

(e) Double check your answer for part c) by changing the coordinates of the new

vector back to standard basis 5 using the other matrix.