1. Lesson 7.6 & 7.7 Inverses of a Square Matrix & Determinant

2. In matrices, the word inverse mean something familiar: MATRIX INVERSE MATRIX = IDENTITY MATRIX You can think of the inverse matrix as the inverse operation much like multiplication and division with real numbers 2 x 2 Identity Matrix:

3. This gives us another way to solve systems: Set this system up with a variable matrix: Let A = the variable coefficient matrix X = the variable matrix B = the constant matrix

4. Then we could simply write AX = B Then solve for X by multiplying both sides by the inverse of A Matrix A and its inverse cancel, and the result of the right side is our answer. Solving on the calculator: Just use the x -1 key with matrix A

5. Example – solve the system

6. Note: We could find the inverse by hand by using an augmented matrix consisting of the coefficient matrix and the identity matrix. Then you would use row operations to change the coefficient matrix (left side) into the identity matrix. The new matrix (right side) will be the inverse.

7. The Determinant A useful number found in patterns when solving systems Consider it an operation in matrices – it is built in the calculator Given matrix A Then the determinant is: Easy to calculate for a 2 x 2 actually. If you are just asked to find the determinant I wouldn’t use the calculator. “Top diagonal product – bottom diagonal product”

8. Symbol for determinant is 2 vertical bars, like absolute value. Example: Find I would use a calculator for this one!