1. Show that the vectors (1/(3√2), 1/(3√√2), –4/(3√√2))¹, (2/3,2/3,1/3), (1/√√2, -1/√√2,0)¹ form an orthonormal basis of R³. Find the coordinates of the vector (1, 4, 3) with respect to that basis.

4) Find a vector perpendicular to both i - 3j + 2k and 5i-j-4k. 5) Find the values of 2 that such that the given equations have non-

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.