Construct a linear tranformation that takes the fundamental triangle with vertices at (0, 0), (1, 0), and (0,1) to the triangle with vertices at (a1, b1), (a2, b2), and (a3, b3). Compare the...

Construct a linear tranformation that takes the fundamental triangle with vertices at (0, 0), (1, 0), and (0,1) to the triangle with vertices at (a1, b1), (a2, b2), and (a3, b3).

Compare the triangular integration rules with a nested integration scheme following  1 0  x 0 f (x, y) dy dx for the posterior in Example 10.2. Use both midpoint and Simpson versions of each.