Let TA:R³ R³ be multiplication by -150 A = 2 1 2 6 7-5 and let e₁,e₂, and e3 be the standard basis vectors for R³. Find the following vectors by inspection. TÃ(е₁), TÃ(е₂), and TÂ(е3) TA(e₁)-(i TA(₂) - (i TA(3) - (i i )

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.