Question

Find the coordinate vector for w relative to the basis:
S = {U1, U2} for r^2,
U1 = (1,0),
U2 = (0,1),
w = (3, -7)

Answer 1

w=3U1-7U2

Answer 2

w is a linear combination of the basis vectors U1 and U2, so we need A and B such that
\[Au_1+Bu_2=w\]since U1 = (1,0), and U2 = (0,1), the obvious linear combination is\[3u_1-7u_2\]