February 01, Matrix Row Operations 2016 ink.notebook. 6.6 Matrix Row Operations. Page 49 Page Row operations
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1 6.6 Matrix Row Operations 2016 ink.notebook Page 49 Page Row operations (Solve Systems with Matrices) Lesson Objectives Page 51 Standards Lesson Notes Page Matrix Row Operations Press the tabs to view details. 1
2 Lesson Objectives Standards Lesson Notes After this lesson, you should be able to solve linear systems by using matrices on a calculator. Press the tabs to view details. Lesson Objectives Standards Lesson Notes N VM.7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. N VM.8. Add, subtract, and multiply matrices of appropriate dimensions. A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Press the tabs to view details. Matrix = numbers arranged in rows and columns The plural is matrices. They are named by a capitol letter. Dimensions = how many numbers going down by how many numbers going across 2 x 3 element = each individual number in the matrix 1. Give the dimensions of each matrix. A = B = C = A = x B = x C = x M = M 21 = 4 4 E = E 32 =
3 6.6 Matrix Row Operations 2016 ink.notebook Augmented Matrix - Consists of the coefficients and the constant terms of a system of equations. The coefficients and the constants are separated by a dashed line. Linear system: 9 Augmented matrix: Find the augmented form of each matrix Row Reduction is a process of performing elementary row operations on an augmented matrix to get the coefficient portion of the matrix to have the form of the identity matrix. We are going to use the calculator to put the augmented matrix into reduced row echelon form. (RREF) 3
4 For both operating systems, you must see the identity matrix to get the correct answers. The numbers on the right after the identity matrix are the x and y values. Equations must be in standard form to be entered into the calculator. 2 nd x 1 fl edit Enter the dimensions: hitting enter after each number Hit enter after each number in the matrix If there is a line as shown below, then the solution is no solution or many solutions. To get the answer to the system: 2 nd x 1 fl math rref( enter 2 nd x 1 A enter ) enter Use an augmented matrix to solve each system of equations. If the system is inconsistent or dependent, say so. = : : nd x 1 fl edit Hit enter after each number 2 nd x 1 fl math rref( enter 2 nd x 1 A enter ) enter 2 nd x 1 fl math rref( alpha zoom. = : : 2 1 Answer: (2, 1) 4
5 Write a system of equations for each augmented matrix
6 6.6 Matrix Row Operations 2016 ink.notebook 12. Mel is having a few friends over and she is buying subs and cans of soda for them. Mel bought 28 items. If Mel spent $56.70, how many subs and how many sodas did she buy? a) If the reduced row echelon form of the augmented matrix for a system of equations is On Your Whiteboards a) many solutions b) no solution c) (0, 0, 1) d) none of these whiteboard 6
7 Use an augmented matrix to solve each system of equations. b) c) On the Worksheet Find the augmented form of each matrix Homework 7
8 Find the augmented form of each matrix. 3. Use an augmented matrix to solve each system of equations Use an augmented matrix to solve each system of equations Use an augmented matrix to solve each system of equations
9 Write a system of equations for each augmented matrix. 13. Write a system of linear equations to model each situation. Then solve. 15. Darnell and Sandra went shopping for graphic novels. The store charges one price for all new books and another for all old books. Find the cost of one old book and one new book
10 16. If the Franklin High School cheerleaders replace 8 uniforms and 6 poms, the cost is $378. If they replace 6 uniforms and 9 poms, the cost is $333. Find the cost of a uniform and a pom. 17. Tasha paid $25.75 for 3 games of miniature golf and 2 rides on go karts. Trevor paid $35.75 for 4 games of miniature golf and 3 rides on go karts. How much did each activity cost? Answers: 10
January 24, Matrix Row Operations 2017 ink.notebook. 6.6 Matrix Row Operations. Page 35 Page Row operations
6.6 Matrix Row Operations 2017 ink.notebook Page 35 Page 36 6.6 Row operations (Solve Systems with Matrices) Lesson Objectives Page 37 Standards Lesson Notes Page 38 6.6 Matrix Row Operations Press the
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