For those that are learning how to use matrices or just need a quick refresher

1. Presented by: Katie Arnold MATRIX OPERATIONS

3. We will then learn about matrix addition matrix subtraction matrix multiplication determinants of 2x2 and 3x3 matrices

5. Each of these numbers is called an entry or an element.

6. The elements of a matrix usually are enclosed by two brackets. Here are some examples. , , ,

8. The size of a matrix is identified by the number of its rows and columns.

10. Each element or entry in a matrix is identified by its location. The location of an entry is the point in which the row and the column to which the entry belongs intersect.

11. Determine the size of the matrix: answer 2x4

13. For example, to add the matrices and compute the following:

14. Sum of entries in first rows and first columns = 3 + 1 = 4

15. Sum of the entries in first rows and second columns = 8 + 0 = 8

16. Sum of entries in second rows and first columns = 2 + 2 = 4

17. Sum of entries in second rows and second columns = 11 + 3 = 14 Now, we have all the entries of the resulting matrix. So,

19. For example, to add the matrices and compute the following:

20. Difference of entries in first rows and first columns = 3 - 1 = 2

21. Difference of the entries in first rows and second columns = 8 - 0 = 8

22. Difference of entries in second rows and first columns = 2 - 2 = 0

23. Difference of entries in second rows and second columns = 11 - 3 = 8 Now, we have all the entries of the resulting matrix. So,

25. In that case the product Amxnx Bnxr will result in a matrix of size mxr

26. Let ; we are trying to compute In this case, the coefficients of matrix C will be computed as follows:

29. The determinant of a matrix is shown by placing the entries of the matrix between two vertical bars | |

30. For example the determinants of matrix is