1. Matrix Operations

2. Matrix Notation

3. Example

4. Equality of Matrices

5. Square Matrix

6. Diagonal Matrix

7. Triangular Matrices

8. Row and Column Vectors

9. Transposition of Vectors

10. Transposition of Matrices

11. Example

12. Symmetric and Skew-Symmetric Matrices

13. Addition of Matrices

14. Scalar Multiplication

15. Zero Matrix

16. Properties of Additon

17. Properties of Scalar Multiplication

18. Properties of Tranposition

19. Product of Matricies

21. Identity Matrices

22. Identity Property

23. A System of Linear Equations

24. The Matrix Equation Ax=b

25. Properties of Matrix Multiplication

26. Cautions

27. Matrix Powers

28. Theorem

29. Properties of Transposition

30. Definition of Linear Combination

31. Consistency Theorem for Linear Systems A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.

32. Definition

33. Matrix Inverse Identities