1. 4.5 Solving Systems using Matrix Equations and Inverses

2. Matrix Equation A linear system can be written as a matrix equation AX=B Coefficient matrix Variable matrix Constant matrix

3. Ex. 1 Write as a matrix equation.

4. Suppose ax = b How do you solve for x? We cannot divide matrices, but we can multiply by the inverse. AX = B A -1 A -1 IX = A -1 B A -1 X = A -1 B Solving Matrix Equations

5. Ex. 2 Solve using matrices. x = -7 y = -4 A B A -1 X = A -1 B AX = B (-7, -4)

6. Ex. 3 Solve using matrices x = 5/7 y = 2 (5/7, 2)

7. Ex. 4 Solve using matrices x = 2 y = -1 z = -2 (2, -1, -2)

8. Ex. 5 Solve using matrices x = 4 y = -7 z = 2 (4, -7, 2)

9. Assignment