Section 9.4 Systems of Linear Equations: Matrices Objectives: Define- matrix, dimension, row, column. Find the augmented matrix of a linear system.

Definition of a matrix – An m x n matrix is a rectangular array of numbers with m rows and n columns.

We say the matrix has dimension m x n. The numbers amn are the entries of the matrix. The subscript on the entry amn indicates that it is in the mth row and the nth column.

Matrix Dimension Here are some examples. 2 rows by 3 columns 1 row by 4 columns

Class Work State the dimension of each matrix. 1. 2. 3.

Augmented Matrix of a Linear System We can write a system of linear equations as a matrix by writing only the coefficients and constants that appear in the equations. This is called the augmented matrix of the system.

Linear System Augmented Matrix

Ex 1. Write the augmented matrix of the system of equations.

Class Work 4. Write the augmented matrix of the system of equations.

Ex 2. Write the system of equations for the given augmented matrix Ex 2. Write the system of equations for the given augmented matrix. Then solve the system.

Ex 3. Write the augmented matrix of the system and solve the system.

Class Work 5. Write the augmented matrix and solve the system.

Class Work 6. Write the system of equations for the given augmented matrix. Then solve the system.

HW p 673 1-6 (state the dimension), 15-23 odd, 47 (write the augmented matrix and then solve the system)