In Algebra 2 we learned to solve systems of equations with more than two variables. Generally the technique used was elimination. The goal was to get a system that looked like: X + Y+ Z = 6 X - Y + Z = 2 2X - Y + Z = 3 Into a format where we had a triangular row of zeros such that the system was modified to look like: X + Y + Z = 6 Y + Z = 5 Z = 3 (where the coefficients for the missing variables were 0) This allows us to use the value of Z to solve for Y and then to use Y and Z to solve for X. We can also represent this format in matrix format which allows for a shorthand way to write the system as well as various shorter methods to solve systems of equations using matrices. The first assignments and videos below review the solving of a system of equations using elimination without matrices. The next section than represents a way to solve similar systems of equations in matrix format. 9.3 Several Variables pp.657 – 58: 6, 8, 10, 16, 20 9.3 (cont-d) p. 658: 15, 17, 19, 25, 31 9.3 Dependent p.658: 18, 22, 24, 26, 30 These problems should be completed by Thursday, May 7. System of equations with 3 variables part 1 www.youtube.com/watch?v=wIE8KSpb-E8 System of equations with 3 variables - part 2 www.youtube.com/watch?v=5FvY8XLrqmM Examples solving systems using elimination: www.youtube.com/watch?v=3RbVSvvRyeI&feature=youtu.be www.youtube.com/watch?v=EytTXf8_KYA&feature=youtu.be No solution Case www.youtube.com/watch?v=ryNQsWrUoJw&feature=youtu.be Infinite Solution Case www.youtube.com/watch?v=mThiwW8nYAU&feature=youtu.be The notes and answer keys for these problems are at the very end of this post. Representing Systems using Matrices 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: Monday 5/11/20 Homework: Text page 674: #'s 30, 34, 38, 42 Due: Tuesday 5/12/20. (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. lesson_plan_-_section_9.4_-_matrices_-_day_1.pdf Download File answer_key_-_section_9.4_-_matrices_day_1.pdf Download File answer_key_-_section_9.4_matrices_day_2.pdf Download File
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