The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.

1. Presented by: Katie ArnoldMATRIX OPERATIONS

2. Preview of things to comeWe will begin reviewing what we know about matrices

3. We will then learn about matrix addition matrix subtractionmatrix multiplicationdeterminants of 2x2 and 3x3 matrices

4. Introduction to MatricesA matrix (plural: matrices) is a rectangular array of numbers.

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. , , ,

7. Introduction to Matrices (continued)The horizontal lines of a matrix are called rows and the vertical lines are called columns.

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

9. The size of a matrix is denoted as an index for the label of the matrix. The index usually is in the form of m × n in which m is the number of rows and n is the number of columns. Introduction to Matrices (continued)For example, S4 × 3 represents a matrix S, which has four rows and three 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

12. ADDING MATRICESAdding two or more matrices is a simple task. They just must have the same size. Then, adding the corresponding entries of the given matrices results in the addition of the matrices.

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