Lesson 11-1 Matrix Basics and Augmented Matrices

Objective: To learn to solve systems of linear equation using matrices.

Matrices A rectangular array of numbers is called a

matrix (plural is matrices) It is defined by the number of rows (m) and

the number of columns (n) “m by n matrix” Example: is a 2 x 3 matrix

1 0 52 3 4

Matrices Each number in the matrix has a

position A =

Each item in the matrix is called an

element

a 11 a 12 a

13a 21 a 22 a

23

What is the dimension of each matrix?

67237

89511

36402

3410

200

318 0759

20

11

6

0

7

9

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)

Warm-UpGive the dimensions of each matrix.

1)

5 0 7 11

0 3 7 192)

15 7

10 9

6 6

Identify the entry at each location of the matrix below.

3) b12

7 0 13

2 4 2

12 1 10

4) b21

5) b32

Warm up Find the dimensions of the following matrices: 1. 2.

3. For the first matrix find a21

444023

6031054

325

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

111

208

4

Augmented matrix has the coefficients of all the variables (in order) along with the answers in the last column.

Using the Calculator to Solve [2nd] [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 [2nd] [matrix] MATH scroll down to B: rref [ENTER] [2ND] [MATRIX]

[A] [ENTER] You will get a new matrix - the last column is

your answer for x, y and z.

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