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Linear Equations and Matrices by Meghan Kimber

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Target Audience This lesson is intended for college freshmen in Finite Mathematics 1160

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Objectives To create coefficient, constant, and augmented matrices from linear equations To understand and use double subscript notation To be able to write linear equations given a matrix Identify methods to solve a system of linear equations

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From Linear Equations to Coefficient Matrices Example 1: 3x - 2y = 10 -6x + 4y = -7 Example 1: 3x - 2y = 10 -6x + 4y = -7 A = 3 -2 -6 4 You Try 1: -2x - 2y = 10 7x + 5y = -3 You Try 1: -2x - 2y = 10 7x + 5y = -3 B = -2 -2 7 5 B = -2 -2 7 5

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From Linear Equations to Constant Matrices Example 2: 3x - 2y = 10 -6x + 4y = -7 Example 2: 3x - 2y = 10 -6x + 4y = -7 A = 10 -7 You Try 2: -2x - 2y = 10 7x + 5y = -3 You Try 2: -2x - 2y = 10 7x + 5y = -3 B = 10 -3 B = 10 -3

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From Linear Equations to Augmented Matrices Example 3: 3x - 2y = 10 -6x + 4y = -7 Example 3: 3x - 2y = 10 -6x + 4y = -7 A = 3 -2 10 -6 4 -7 A = 3 -2 10 -6 4 -7 You Try 3: -2x - 2y = 10 7x + 5y = -3 You Try 3: -2x - 2y = 10 7x + 5y = -3 B = -2 -2 10 7 5 -3 B = -2 -2 10 7 5 -3

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From an Augmented Matrix to Linear Equations Example 4: A = -4 8 53 -1 5 -7 A = -4 8 53 -1 5 -7 You Try 4: B = -22 -4 17 -6 5 9 B = -22 -4 17 -6 5 9 Equations: -4x + 8y = 53 -1x + 5y = -7 Equations: -4x + 8y = 53 -1x + 5y = -7 Equations: -22x - 4y = 17 -6x + 5y = 9 Equations: -22x - 4y = 17 -6x + 5y = 9

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Double Subscript Notation Double subscript notation describes the location of a number in a matrix The first subscript number represents the row and the second subscript number represents the column Generally: A row#column# or A

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Double Subscript Notatioin Identify the following values or positions: A 23 = 8 = A 12 = -3 = Identify the following values or positions: A 23 = 8 = A 12 = -3 = A = 3 -2 -3 -6 4 7 -8 8 1 A = 3 -2 -3 -6 4 7 -8 8 1 7 -2 7 -2 A 32 A 13 A 32 A 13

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Methods to Solve a Linear System or Matrix Graphing Elimination Eliminating a variable algebraically Row Operations Interchanging rows Multiplying a row by a constant Multiplying a row by a constant and adding it to another row Graphing Elimination Eliminating a variable algebraically Row Operations Interchanging rows Multiplying a row by a constant Multiplying a row by a constant and adding it to another row

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Objective Review? If you’d like to review the objectives, click the button below.

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Good luck on the quiz! http://TeacherWeb.com/MN/Universityo fMinnesota-Duluth/Kimber1160/ http://TeacherWeb.com/MN/Universityo fMinnesota-Duluth/Kimber1160/ http://TeacherWeb.com/MN/Universityo fMinnesota-Duluth/Kimber1160/ http://TeacherWeb.com/MN/Universityo fMinnesota-Duluth/Kimber1160/

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