Suppose the basis of an existing system are e1 = [1 0]T (transpose) and e2 = [0 1]T, respectively. Now, assume we have a new set of basis, which are f1 = e1 + e2 and f2 = e1 − e2.
• For x1 = 2f1 + 3f2, find a1 and a2 such that x1 = a1e1 + a2e2.
• For x2 = e1 − 3e2, find b1 and b2 such that x2 = b1f1 + b2f2.