The set is a basis for R². Find the coordinates of the vector a = [*]B= 0 [-24] relative to the basis B. B-(3-D) =

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)

Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (9, -2, -3) in terms of the ordered basis B = {i,j,k}. [(9,-2,-3)]B= b. Represent the vector (9, -2, -3) in terms of the ordered basis C = {3, e1, e2}. [(9,-2,-3)] c = c. Represent the vector (9, -2, -3) in terms of the ordered basis D= {-2, -1, e3}. [(9,-2,-3)]D =

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.

Suppose the vector x characterizing the antigenic state of an influenza virus population changes from one season to the next according to the equation 23 Xt + 1 ¹ -[3.39]** 0 0.9 If the vector in the current season is [...] what was the vector in the previous influenza season? ↓ 1

Find the vector x determined by the given coordinate vector [x] and the given basis B. Illustrate the answer with a figure. 2 -CH-)--[] [X]B = -1 B= 1 1 3 2