Download presentation

Presentation is loading. Please wait.

Published byNorma Jackson Modified over 6 years ago

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” EExample: 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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google