Answer to Question #58697 in Linear Algebra for esita

Question

Let B = far a2, a3) be an ordered basis of
R3 with al = (1, 0, -1), a2 = (1, 1, 1),
a3 = (1, 0, 0). Write the vector v = (a, b, c) as
a linear combination of the basis vectors
from B.
(b) Suppose al = (1, 0, 1), a2 = (0, 1, -2) and
a3 = (-1, -1, 0) are vectors in R3 and
f : R3 -> R is a linear functional such that
f(al) = 1, f(a2) = -1 and f(a3) = 3. If
a = (a, b, c) E R3, find f(a).