1. Fundamentals of Engineering Analysis
EGR 1302 The Inverse Matrix

2. Solving Systems of Linear Equations
The Inverse Matrix
Anxn and Bnxn are Square Matrices of the same Order.
A * B = In
B * A = In
B is called “The Inverse of A”
in Algebra, the equivalent is
B = A-1
A * A-1 = I

3. Solving Systems of Linear Equations
Sum of Products
The same equation can represent any Order.

4. Solving this System for x1, x2
( )
( )
Becomes
Subtract

5. Solving this System for x1, x2 (cont.)
factor out
the denominator
Sum of Products
A new Matrix “C”

6. The Solution to
We now have a solution for the Inverse of a 2x2 Matrix

7. The Determinant
The Determinant of A =

8. Rules for Finding the Inverse of a 2x2 Matrix
Rule 1: Swap the Main Diagonal
Rule 2: Change Signs on
the Back Diagonal
Rule 3: Divide by
the Determinant

9. Review of the Solution to a 2x2 System
Is solved by
If there is no solution
Stay Tuned!

10. A Numerical Example
Becomes

11. Questions?