1. Agenda Textbook / Web Based Resource Basics of Matrices Classwork
11/14/2018
Agenda
Textbook / Web Based Resource
Basics of Matrices
Row-Echelon Form
Reduced Row Echelon Form
Classwork
Homework
INSERT HERE

2. Matrices & Linear Systems
11/14/2018
Matrices & Linear Systems

3. By the End of the Day: You should know how to:
11/14/2018
By the End of the Day:
You should know how to:
Determine the Order of a matrix
Perform Elementary Row Operations
Identify Elementary Row Operation
Identify if a Matrix is in Row-Echelon Form
Identify if a Matrix is in Reduced Row-Echelon Form

4. 11/14/2018
Definitions
Matrix:
a rectangular array of numbers. Each number is called an entry
Order of a matrix:
Tells you how many rows and columns the matrix has. If a matrix has m rows and n columns then it is an m x n matrix.
Square matrix
Matrix which has the same number of rows and columns

5. Order of a Matrix 11/14/2018 Try These… 2) 1 x 2 4) 5 x 1 6) 3 x 3
This is a 3 x 4 matrix
The 2,3 entry is: 5

6. Row Operations There are 3 Elementary Row Operations: 11/14/2018
Interchange two rows
Multiply a row by a non zero constant
Add a multiple of a row to another row

7. 11/14/2018
Row Operations
Interchange 2 Rows:
Interchange R1 and R3:

8. Row Operations 2. Multiply a row by a non zero constant:
11/14/2018
Row Operations
2. Multiply a row by a non zero constant:
Multiply R2 by -2:

9. Row Operations 3. Add a multiple of 1 row to another row:
11/14/2018
Row Operations
3. Add a multiple of 1 row to another row:
Add 3 * R1 to R2
3(2) + 4 = (-1) + 5 = 2
3(-2) + 2 = (3) + 8 = 17

10. Row Operations To Determine what row operations occurred:
11/14/2018
Row Operations
To Determine what row operations occurred:
Identify which row changed
If 2 changed, they were probably interchanged
Determine if each number is the result of multiplying each number by a constant
Determine the constant
Determine how much was added to each entry to get the row.
Determine which row must have been multiplied to get these numbers, and by how much.

11. Row Operations What row operation was performed? 11/14/2018
Which row changed?
Was it mult by a constant?
How much was added?
Which row was multiplied?
What is the row operation?
performed? R3 No
4, -4, -2, 6
R1 (by 2)
Add 2 * R1 to R3

12. 11/14/2018
Row Operations
When doing Row-Echelon reduction method there may be more than one operation required.
3*R1 + R2
2*R1 + R2
5*R1 + R3

13. Still Makes the “Staircase”
11/14/2018
Row-Echelon Form
A matrix is in row echelon form if:
Any rows consisting of entirely zeros occur at the bottom of the matrix
For each row that does not consist entirely of zeros, the first nonzero entry is a 1
As you work down the matrix the “leading 1” moves to the right.
Still Makes the “Staircase”

14. 11/14/2018
Row-Echelon Form
Row Echelon Form
Not Row-Echelon Form

15. 11/14/2018
Row-Echelon Form
A matrix is in reduced row echelon form if every entry above and below a leading 1 is 0.
Reduced Row Echelon Form
Not Reduced Row-Echelon Form

16. Row-Echelon Form You Try These on Your Own: 11/14/2018
INSERT YOUR PROBLEMS HERE

17. ü ü ü ü ü It’s the End of the Day: Do you know how to:
11/14/2018
It’s the End of the Day:
Do you know how to:
Determine the Order of a matrix?
Perform Elementary Row Operations?
Identify Elementary Row Operation?
Identify if a Matrix is in Row-Echelon Form?
Identify if a Matrix is in Reduced Row-Echelon Form? ü ü ü ü ü

18. 11/14/2018
Homework
Study:
INSERT HERE
Do:
Read & Take Notes:

19. Resource Credits Justin Bohannon
11/14/2018
Resource Credits Justin Bohannon