Chapter 5: Matrices and Determinants Section 5.5: Augmented Matrix Solutions

 Goal: To solve a system of linear equations in three variables using the augmented matrix method

Section 5.5: Augmented Matrix Solutions  Augmented matrix: formed by writing a system of equations that is in standard form as a matrix using the coefficients and the constants Ex: 2x – y + 3z = x + z = x + 5y =

Section 5.5: Augmented Matrix Solutions  We know how to solve a system of equations with more than 2 variables and 2 equations by executing the elimination method repetitively until all variables have been solved for

Section 5.5: Augmented Matrix Solutions  To solve a System of Three Linear Equations Using Augmented Matrices  Using a row operation, if necessary, make the element in the first row, first column 1  Add multiples of the first row to the second and third rows to make the other the other elements in the first column 0’s  Using a row operation, if necessary, make the element in the second row, second column 1

Section 5.5: Augmented Matrix Solutions  Continued…  Add multiples of the second row to the first and third rows to make the other elements in the second column 0’s  Using a row operation, if necessary, make the element in the third row, third column 1  Add multiples of the third row to the first and second rows to make the other elements in the third column 0’s  The last column of the matrix are the values of x, y, and z respectively

Section 5.5: Augmented Matrix Solutions  Refer to “4.4 Homework Worksheet”  Example 1 2x + 5y + 3z = 4 4x – 6y + 9z = 39 x + 2y – 7z = -40

Section 5.5: Augmented Matrix Solutions  Example 2: x – 4y – z = 15 3x + y – 5z = -11 x – 3y + 3z = 19

Section 5.5: Augmented Matrix Solutions  Example: Pg. 225 #9  Homework: Pg. 224 #1-6 (all)