The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]); v2:=vector([1/sqrt(2),1/sqrt(2),0]); v3:=vector([-1/sqrt(2),1/sqrt(2),0]); The coordinates of the vector w:=vector([1,-1,1]) with respect to the basis vectors v1, v2 and v3 of R3 are

7) Find all vectors v in F such that 2v + (C) = (5)

Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V, = (2, 2, -1) V2 = (-1, -2, 1) V3 = (1, -1, 1)

Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v = (13,54); B = {(1,0), (0, 1)} for R². (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.