Find a set of vectors {ū, v} in R* that spans the solution set of the equations w – x 4z 0, 2w + 2x + y – 2z 0. - u =

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.

Find two vectors Vy and V2 whose sum is (-5, –3), where 7y is parallel to (2, 5) while Uz is perpendicular to (2, 5).

2. Find the equation of the plane that is parallel to the vectors and contains the points (-2, 3, -1) and (2, 0, 1).