1. Honor Trig/MA
Inverses of 2 X 2 Matrices

2. Inverse Transformations
2 Transformations, S and T, are inverse transformations if and only if S◦T = T◦S =

3. ad – bc If the determinant is = 0, then NO INVERSE EXISTS!
recall: Determinant
ad – bc
If the determinant is = 0,
then NO INVERSE EXISTS!

4. Example
Show that the following 2 matrices are inverses: (SHOW THE INTERMEDIATE STEP!)

5. How do I find the inverse of a matrix?
Step 1: Find the determinant! if it is equal to 0. Step 2: Perform the “switch”: Step 3: Multiply this matrix by 1/determinant

6. Find the inverse of Determinant: 1(4) - -3(5) = 19 “Switch” Multiply:
Example
Find the inverse of Determinant: 1(4) - -3(5) = 19 “Switch” Multiply:

7. A Couple of Notes about Inverses….
You may need to reduce the fractions after multiplying by 1/determinant! Do not leave as decimals: integers or fractions ONLY. You can check your answer in the calculator: Enter the matrix into calculator [A]-1 = inverse of a matrix MATH, FRAC, ENTER

8. Using Matrices to Solve A System
Ax + By = C Dx + Ey = F Put into matrix form: Multiply by the inverse of coefficient matrix:

9. x=1 and y=1 Solve the system using matrices: 2x + 2y = 4 2x + y = 3
Example
Solve the system using matrices: 2x + 2y = 4 2x + y = 3
x=1 and y=1

10. More Practice
1. Find the inverse of the following matrix: . 2. What would n have to be in the following matrix in order for the inverse to NOT exist? 3. Solve the system using matrices: 4x + 3y = 17 3x – 4y = 19

11. Closure
Refer to the Cramer’s Rule Warm-Up. Verify your result by solving the system using the matrix method in this lesson.