1. Lesson 11-1 Matrix Basics and Augmented Matrices Objective: To learn to solve systems of linear equation using matrices.

2. Matrices  A rectangular array of numbers is called a matrix (plural is matrices)  I It is defined by the number of rows (m) and the number of columns (n) “m by n matrix” EExample: is a 2 x 3 matrix 1 0 5 2 3 4

3. Matrices  Each number in the matrix has a position A =  Each item in the matrix is called an element a 11 a 12 a 13 a 21 a 22 a 23

4. What is the dimension of each matrix? 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also called a column matrix)

5. Warm-Up Give the dimensions of each matrix. 1) 2) Identify the entry at each location of the matrix below. 3) b 12 4) b 21 5) b 32

6. Warm up  Find the dimensions of the following matrices:  1. 2.  3. For the first matrix find a 21

7. Augmented Matrices  System of Linear Equation  x -2y + 2z = -4  x + y – 7z = 8  -x -4y + 16z = -20  expressed in a matrix : -2 2  1 -7  -4 16 Augmented matrix has the coefficients of all the variables (in order) along with the answers in the last column.

8. Using the Calculator to Solve  [2 nd ] [matrix] EDIT[ENTER]  MATRIX [A] IS A 3 x 4 matrix (3 rows x 4 columns)  then enter all the data into the matrix  Once data is entered, quit then  [2 nd ] [matrix] MATH  scroll down to B: rref [ENTER] [2 ND ] [MATRIX] [A] [ENTER]  You will get a new matrix - the last column is your answer for x, y and z.

9. Practice:  1. 4x + 6y = 0 2. 6x - 4y + 2z = -4 3. 5x - 5y + 5z = 10  8x - 2y = 7 2x - 2y + 6z = 10 5x - 5z = 5  2x + 2y + 2z = -2 5y + 10z = 0