-0 V₁ = V2 = [f] = = 1 7 1 -3 1 "-(⠀) -1 -3 2 -1 -32, Find the image vectors f (v₁), f (v₂), f (√3) form a basis of R3 (b) Consider a linear map ƒ : R³ → R3 and suppose the matrix associated with ƒ under the standard basis of R3 is given by: V3 = 1

A snack company is preparing two mixtures of snacks from a supply of 110 pounds pretzels, 30 pounds pistachios, 10 pounds cheese puffs, 60 pounds sesame sticks, and 20 pounds toffee bites. Mixture X contains 55% pretzels, 20% pistachios, 5% cheese puffs, 20% sesame sticks, and no toffee bites, and sells for $7.99 per pound. Mixture Y contains 45% pretzels, 10% pistachios, no cheese puffs, 10 % sesame sticks, and 15% toffee bites, and sells for $5.99 per pound. If x = # of pounds of Snack X and y = # of pounds of Snack Y, determine the constraints on this linear programming problem. Inequality for pretzels [ Choose ] Inequality for pistachios ( Choose] Inequality for cheese puffs ( Choose ) Inequality for sesame sticks [Choose ] Inequality for toffee bits [ Choose ) Non-negativity inequalities [ Choose ] >

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

Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x - y) from R2 --> R2, find the coordinate vectors of basis C in terms of basis B.