Mathematica Tutor

Part 9: Solving systems of linear equations

1. How hard is it to solve linear equations? First, make sure the variables x, y, and z are unassigned:
   x=.
   y=.
   z=.
   Then enter
   {x+4*y+3*z==10, 2*x+y-z==-1, 3*x-y+z==11}
   and
   Solve[%]
   Impressed?
   
   
2. You don't have to trust Mathematica's calculations any more than you would trust your own. Assign the answers to the variables (you can edit the unassign lines in Step 1), and re-enter the line that defines the equations. Satisfied?
   
   
3. Unassign your variables again, and ask Mathematica to solve
   

   2x + 3y - 7z + w = 8

   4x - 2y + z + 2w = 4

   5x + y - 4z + 3w = 6

   
   (Don't forget to use double equals signs!)
   
   

4. What do you think about the solutions in Step 3? What do they mean? Did you get a warning message? What do you think that meant? Copy your input line that defines the equations to a new line, and enter it again -- so it becomes the "last result" again. Then enter
   Solve[%, {x,y,z}]
   How does the second set of solutions compare to the first? How could you check that the two sets of solutions are equivalent? Do it.