2. Linear Equations and Matrices by Meghan Kimber

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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 

10. 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

11. 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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13. 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/