Math 3191 Extra Homework #3

1. Use matrix inverses to solve the following systems of equations.
                              7x + 4y - 2z  = 8
(a)                          4x +7y + 5z  = 5
                              2x -3y + 8z   = 2

                              2x -5y + z   = a
(b)                          7x -y + 5z   = b
                              3x -6y + 5z = 9

                              ax + 4y + 2z  = 8
(c)                          3x + by - 5z  = 1
                              4x + 3y + cz  = 3
2. For what values of s and t does have an inverse?

3. Suppose that neither has an inverse. Find s and t.

4. Let . Solve the following equations for the 3 by 3 matrix A.