Suppose f: R² → R² is a linear transformation. The two pictures on top in the figure use standard S-coordinates, where S = {e₁,e₂}. The two figures on bottom in the figure use B-coordinates, where B = {b₁,b₂}. The figure shows the vectors b₁ and b₂ in blue and the vectors f(b₁) and f(b₂) in red. Standard basis S= {e₁,e₂} y 4 3 2 1 -1 -2 -9 -4 -4-3-2-1 b1 b1 b2 [id] ↑ 19 1 2 3 b2 Custom basis B = {b₁,b₂} 4 X [f]'s [f] B →> 4 3 2 1 -1 -2 -9 -4 Standard basis S = {e₁,e₂} y -4-3-2-1 f(b2) पं b1 b2 19 1 2 [id] ↑ b1 b2 44 (b1) 3 4 Custom basis B= {b₁,b₂} X

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 =

2. Find the coordinate vector [x] of a relative to the given basis B = {b₁,b2, b3} . b₁ = -1 , b₂ = -3 4 9 b3 = 2 -2 4 ,x= 8 -9 6

Find the coordinate vector [x]R of the vector x relative to the given basis B. 5 - 25 b = 5 , b2 = - 3 X = - 1 and B = %3D - 4 - 3 17 O A. - 2 - 3 О В. - 250 - 2 - 119 О с. - 130 – 122 103 O D. - 2 – 4

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