1. 4.5 Solving Systems using Matrix Equations and Inverses OBJ: To solve systems of linear equations using inverse matrices & use systems of linear equations to solve real-life problems

2. 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 8x = 24 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 DO NOT COPY 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 x = 5/7 y = 2 (5/7, 2)

7. Ex 4: Solve using matrices x = 2 y = -1 z = -2 (2, -1, -2) Ex 5: Solve using matrices x = 4 y = -7 z = 2 (4, -7, 2)