Solve the following problems using Matlab or Scilab (Commands might vary) . Turn in an electronic diary of the work. Include a cover page with your name, ID, and section.
1. Let A be the coefficient matrix and B the right-hand side of the linear system
3x + 3y + 12z = 18
x + y + 4z = 6
2x + 5y + 20z = 30
-x + 2y + 8z = 12
Enter the matrices A and B and form an augmented matrix C for this system by using the MATLAB command C = [ A B]. Solve the system using rref
2. Use MatLAB command A/B to solve the linear system
16x - 120y + 240z - 140w = - 4
-120x + 1200y - 2700z + 1680w = 60
240x - 2700y + 6480z - 4200w = -180
-140x + 1680y - 4200z + 2800w = 140
You can display more significant digits of the answer by entering format long before solving the system. Return to the standard format by entering format short.
3. Use MatLAB to find a sixth-degree polynomial that fits the points (0,0), (-1, 4.5), (-2, 133), (-3, 1225.5), (1, -0.5), (2, 3), (3, 250.5)