1. Warm Up Multiply the matrices. 1. Find the determinant. 2. –1 Welcome! I’m so glad you’re here! Please get your Calculator. Please get started on this Warm Up! You have 7 minutes.

2. Solve systems of equations using inverse matrices. Objectives

3. To solve systems of equations with the inverse, you first write the matrix equation AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. You can use the inverse of a matrix to solve a system of equations. This process is similar to solving an equation such as 5x = 20 by multiplying each side by, the multiplicative inverse of 5.

4. The matrix equation representing is shown.

5. To solve AX = B, multiply both sides by the inverse A -1. A -1 AX = A -1 B IX = A -1 B X = A -1 B The product of A -1 and A is I.

6. Matrix multiplication is not commutative, so it is important to multiply by the inverse in the same order on both sides of the equation. A –1 comes first on each side. Caution!

7. Example 3: Solving Systems Using Inverse Matrices Write the matrix equation for the system and solve. Step 1 Set up the matrix equation. Write: coefficient matrix  variable matrix = constant matrix. A X = B Step 2 Find the determinant. The determinant of A is –6 – 25 = –31.

8. Example 3 Continued. X = A -1 B Multiply. Step 3 Find A –1. The solution is (5, –2).

9. Check It Out! Example 3 Step 1 Set up the matrix equation. A X = B Step 2 Find the determinant. The determinant of A is 3 – 2 = 1. Write the matrix equation for and solve.

10. Check It Out! Example 3 Continued Step 3 Find A -1. The solution is (3, 1). X = A -1 B Multiply.

11. Homework! Holt 4.4 p. 282 #10-12, 22-24