#Attendance Question 1:
#Who made Fractals a household name
#Probably Benoit Mandelbrot. The Manelbrot set is
with(LinearAlgebra);#Attendance question
#For the equation
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#Then, express any arbitrary vector in R^2 as a linear combination of the 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