Problem 2 Consider the equation of a plane written as a1x+a2y+a3=z. Given three known points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3),write the system of equations that determine a1, a2, and a3. Write a plane function that returns the ai given any three points. Test your function by finding the equation of the plane passing through (1,0,0), (0,1,0), and (0,0,1). What are the values of z at (x,y)=(0,0.5) (0.5,0), (0.25,0.25), and (0.5,0.5)?

Language is Matlab.