Consider \(\mathbb{R}^2\) and the two basis sets A, B of \(\mathbb{R}^2\)
A = \{ (2,3), (1,1) \}
B = \{ (5,2), (3,1) \}
GIVEN: \begin{bmatrix} x \end{bmatrix}_A = \begin{bmatrix} -1 \\ 3 \end{bmatrix}
FIND: \begin{bmatrix} x \end{bmatrix}_B
Let E = \{ (1,0), (0,1 \}
HINT: P_B^A = P_B^E P_E^A