The document discusses finding and using the inverse of a square matrix to solve systems of linear equations. It defines a multiplicative inverse as a matrix whose product with the original matrix results in the identity matrix. It also notes that for a 2x2 matrix, the inverse exists if and only if the determinant is not equal to 0. Examples are provided to find the inverse of 2x2 and 3x3 matrices and to use the inverse to solve systems of linear equations.

1. 8.3 The Inverse of a
Square Matrix
Objective: Find and use the inverse
matrix to solve systems of linear
equations.
Standard: Linear Algebra 9.0

2. What's a MULTIPLICATIVE
INVERSE??

3. To be an inverse matrix:

4. Ex. 1) Show that B is the Inverse of A.

5. Do all matrices have an inverse?
Singular:
Nonsingular (aka: ________)

6. Ex. 2) Find the inverse of A if it exists.
A=

7. The "Shortcut" for a 2x2 matrix
If… and…
ad – bc ≠ 0
then…

8. Ex. 2 Revisited) Find the inverse of A if
it exists.
A=
Ex. 3) Find the inverse of A if it exists.

9. Inverse of a 3x3 Matrix

10. Using Inverses for Systems
of Equations
The coefficient matrix…

11. Ex. 4) Solve the systems using matrices.

12. Ex. 5) Solve the system using matrices.

13. Assignment:
#12 p. 608 #4, 6, 11, 15,
17, 20, 25, 27, 53, 60, 63
Quiz #3 (8.2 and 8.3) on
Tuesday/Wednesday Feb. 22-23