Question 3. In Fishers linear discriminant analysis, we search for a vector w such that all data points are well separately after they are projected to the direction defined by w. When the input data points are

x₁=(4,3)^T y₁ = 1

x₂=(2,2)^T y₂ = 1

x₃=(1,1)^T y₃ = -1

x₄=(-2,-1)^T y₄= -1

(Note that the first element in vector x_i is NOT x₀=1 in this problem), Use Python to find a vector w=[w₁,w₂] with Fishers linear discriminant analysis and provide the intermediate steps