Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin. (a) A(1,3), B(4,4) (b) A(1,-2,0), B(1, -2,3) (c) A(4, 0, -2), B(4, 2, 1) Find the sum of the given vectors and illustrate geometrically. (a) <2,3>, <3, -4> (b) < 1,0, 1>, <0,0,1> (c) <0,3,2 >, < 1,0, -3>

Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, –-20, -3) $1 + u = (4, 5 -10, 2) 41 75 (b) (c) (-4, -14, 23, 37) w = 8 1 + (4) z- (14, -3, 7, 4) (d) z = z =

Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, 1, 3), (5, 0,4)} (a) z = (11,-8, 20) Z = (b) V = (c) W = (d) u = v = (18,-1, 50) W = (4, -7, 13) S₁ + u =(3, 1, -1) S₁ + )$₁ S1 + S₁ + ) $₂ S2

4 and 5, please.