1. Matrices and Matrix Solutions

2. Solving Equations With Matrices

3. Fundamental Concepts

4. Types of Matrices

5. Matrix Types, Continued

6. Matrix Types, Continued

7. Matrix Transpose
Process of interchanging rows and columns

8. Matrix Equality

9. Matrix Addition

10. Matrix Addition Properties
I. COMMUTATIVE PROPERTY:
A + B = B + A
II. ASSOCIATIVE PROPERTY:
A + (B+C) = (A + B) + C
NOTE: Thus order of operation in addition is not important!

11. Matrix Multiplication

12. Matrix Multiplication Properties

15. Representing Equations Using Matrices

16. Solving Equations By Matrix Inverse

17. Example of Matrix Solution

19. Inverse of a 2x2 Matrix Note: the determinant of A is: Steps:
1. Flip the diagonals,
2. Negate the off-diagonals, and
3. Divide by the determinant.
4. Matrix is SINGULAR when determinant = 0, and thus has no inverse.

20. Other Methods of Matrix Solution
Inverse by elementary row transformations
Gaussian elimination
Others
For large matrices with many zeros, sparse matrix methods can be used

21. Spreadsheet Functions
TRANSPOSE
MMULT
MINVERSE
The “trick” in Excel is to press <Ctrl><Shift><Enter> simultaneously