Consider the bases B = u1, u2 and B' = u'1, u'2 for R^2, where u1 = [8, 8], u2 = [6, -1], u'1 =

Question

Consider the bases B = u1, u2 and B&#x27; = u&#x27;1, u&#x27;2 for R^2, where u1 = [8, 8], u2 = [6, -1], u&#x27;1 =

Suman K · Accepted Answer

First, we need to find the matrix P_B_B&#x27; that changes the coordinates from basis B to basis B&#x27;.

Consider the bases B = {u1, u2} and B' = {u'1, u'2} for R^2, where u1 = [8, 8], u2 = [6, -1], u'1 = [1, 7], u'2 = [-1, -1]. Compute the coordinate vector [w]B, where w = [3, -3], and use Formula (12) ([v]B' = PB->B'[v]B) to compute [w]B'. [w]B = (?) [w]B' = (?)