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

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- 1. Presented by: Katie Arnold<br />MATRIX OPERATIONS<br />
- 2. Preview of things to come<br /><ul><li>We will begin reviewing what we know about matrices
- 3. We will then learn about </li></ul>matrix addition <br />matrix subtraction<br />matrix multiplication<br />determinants of 2x2 and 3x3 matrices<br />
- 4. Introduction to Matrices<br /><ul><li>A 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.</li></ul> , , , <br />
- 7. Introduction to Matrices (continued)<br /><ul><li>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. </li></li></ul><li>Introduction to Matrices (continued)<br /><ul><li>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: </li></ul>answer <br /> 2x4<br />
- 12. ADDING MATRICES<br /><ul><li>Adding 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:
- 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 </li></ul>Now, we have all the entries of the resulting matrix. So,<br />
- 18. SUBTRACTING MATRICES<br /><ul><li>Subtracting two matrices is also a simple task. They just must have the same size. Then, subtracting the corresponding entries of the given matrices results in the addition of the matrices.
- 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 </li></ul>Now, we have all the entries of the resulting matrix. So,<br />
- 24. MULTIPLYING 2x2 MATRICES<br /><ul><li>Two matrices A and B can only be multiplied if the number of columns of A is equal to the number of rows of B.
- 25. In that case the product Amxnx Bnxr will result in a matrix of size mxr
- 26. Let ; we are trying to compute </li></ul> In this case, the coefficients of matrix C will be computed as follows:<br />
- 27. MULTIPLYING 2x2 MATRICES (continued)<br /><ul><li>Example</li></ul> Then<br />It must be mentioned that and this can easily be checked. <br />
- 28. DETERMINANTS<br /><ul><li> Only square matrices have determinants (m≠n)
- 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 </li></ul> is <br />
- 31. THE DETERMINANT OF A 2x2 MATRIX<br /><ul><li> For a 2x2 square matrix the determinant is defined as below:
- 32. For example, </li></li></ul><li>THE DETERMINANT OF A 3x3 MATRIX<br /><ul><li> For a 2x2 square matrix the determinant is defined as below:
- 33. For example, </li></li></ul><li>Homework Problems<br />Compute the following:<br />

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