1. INVERSE MATRICES TO SOLVE LINEAR SYSTEMS

2. Identity Matrices
An identity matrix is a square matrix that has 1’s along the main diagonal and 0’s everywhere else.
When you multiply a matrix by the identity matrix, you get the original matrix.

3. Inverse Matrices
When you multiply a matrix and its inverse, you get the identity matrix.

4. Inverse Matrices Not all matrices have an inverse!
To find the inverse of a 2 x 2 matrix, first find the determinant.
If the determinant = 0, the inverse does not exist!
The inverse of a 2 x 2 matrix is the reciprocal of the determinant times the matrix with the main diagonal swapped and the other terms multiplied by -1.

5. Inverse of a 2X2 Matrix

6. Inverse Matrices
Example 1:
det(A) = 3(2) – (-5)(-1)

7. Inverse Matrices
Example 2:

8. Solve a Matrix Equation

9. Solve a Matrix Equation

10. Solve a Matrix Equation

11. Example of Inverse Matrices

12. Example of Inverse Matrices

13. Basketball Problem
During the NBA season, Dirk Nowitzki of the Dallas Mavericks made a total of 976 shots and scored 1680 points. His shots consisted of 3-point field goals, 2-point field goals, and 1-point free throws. He made 135 more 2-point field goals than free throws. Use an inverse matrix to find how many of each type of shot he made.

14. Basketball Problem x = 3-point field goals y = 2-point field goals
z = 1-point free throws
x + y + z = 976 shots
3x + 2y + z = 1680 points
y – z = 135

15. Basketball Problem

16. Basketball Problem