## 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.

- (a) CAD = C - D
- (b) C^2(A + 2D) = DA
- (c) 3AD^{-1} = A^2DC (Assume that A is invertible)