A matrix (plural matrices) is a format to represent data. A matrix represents data with rows and columns of numbers. Rows are horizontal and columns are vertical. A matrix can be used to represent a system of equations. Example: 2X + 3Y = 25 4X - 7Y = 22 can be represented in matrix form as _____ _____ | 2 3 25 | The elements of a matrix are enclosed in the | 4 -7 22 | [ ] symbols. ____ ____ Note that the rows represents each of the equations. The columns represent the various variables and the constants in the equation. X's are the first column. Y's are the second column. The constants are the 3rd column. In this first lesson, we will discuss syntax and notation of matrices, representing systems of equations using matrices, and reducing matrices/solving systems of equations using the method of Gauss -Jordan elimination / row-reduction. Homework: Text page 673: #'s 2, 4, 6, 16, 18, 20 Due: Tuesday 5/5/20 Homework: Text page 674: #'s 30, 34, 38, 42 Due: Wednesday 5/6/20. (More practice on matrices.) Videos: Basic notation and description of the order or size of a matrix. www.youtube.com/watch?v=ilFJYjfKYjk&feature=youtu.be Changing an equation into matrix format and then reducing the matrix to row-echelon form using row/reduction or Gauss Jordan elimination. www.youtube.com/watch?v=BWBckWPjfpw Solving a system of equations (2 x 2) using an augmented matrix www.youtube.com/watch?v=V8mb5BFmJO0&feature=youtu.be Solving a system of equations with no solutions using matrices www.youtube.com/watch?v=NgXXKmQHFDg&feature=youtu.be Solving a system of equations with infinite solutions using matrices www.youtube.com/watch?v=9_wGz6zcZ6s&feature=youtu.be Solving a system of three equations using a system of matrices www.youtube.com/watch?v=WiVeiVIu_SM&feature=youtu.be Solving a system of equations using matrices and REDUCED row-echelon form. www.youtube.com/watch?v=-bPPDq0Y8s4 Using the TI-84 matrix menu to enter a Matrix and show row operations on a Matrix www.youtube.com/watch?v=ABY5rYu3Rmc&feature=youtu.be Using the TI-84 to show Matrix operations on the home screen of the calculator www.youtube.com/watch?v=syx9LY7qMgo&feature=youtu.be There are more videos at the page www.mathispower4u.com/alg-2.php if you wish to see more examples. On the page, press the control key and the f key to open up a search box and type matrix to see the list of videos.
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