1. 3/18/2016Agenda Textbook / Web Based ResourceTextbook / Web Based Resource –Basics of Matrices –Row-Echelon Form –Reduced Row Echelon Form ClassworkClasswork INSERT HERE HomeworkHomework INSERT HERE

2. 3/18/2016 Matrices & Linear Systems

3. 3/18/2016 By the End of the Day: You should know how to: Determine the Order of a matrixDetermine the Order of a matrix Perform Elementary Row OperationsPerform Elementary Row Operations Identify Elementary Row OperationIdentify Elementary Row Operation Identify if a Matrix is in Row-Echelon FormIdentify if a Matrix is in Row-Echelon Form Identify if a Matrix is in Reduced Row- Echelon FormIdentify if a Matrix is in Reduced Row- Echelon Form

4. 3/18/2016Definitions 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. 3/18/2016 Order of a Matrix This is a 3 x 4 matrix The 2,3 entry is: 5 Do (FROM TEXT) Dimension: 1 x 2 Dimension: 5 x 1 Dimension: 3 x 3 Dimension: 1 x 1

6. 3/18/2016 Row Operations There are 3 Elementary Row Operations: 1.Interchange two rows 2.Multiply a row by a non zero constant 3.Add a multiple of a row to another row

7. 3/18/2016 Row Operations 1.Interchange 2 Rows: Interchange R1 and R3:

8. 3/18/2016 Row Operations 2. Multiply a row by a non zero constant: Multiply R2 by -2:

9. 3/18/2016 Row Operations 3. Add a multiple of 1 row to another row: Add 3 * R1 to R2 3(2) + 4 = 10 3(-1) + 5 = 2 3(-2) + 2 = -4 3(3) + 8 = 17

10. 3/18/2016 Row Operations To Determine what row operations occurred: Identify which row changedIdentify which row changed –If 2 changed, they were probably interchanged Determine if each number is the result of multiplying each number by a constantDetermine 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 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. 3/18/2016 Row Operations What row operation was Which row changed? Was it mult by a constant? How much was added? Which row was multiplied? What is the row operation? performed?R3No 4, -4, -2, 6 R1 (by 2) Add 2 * R1 to R3

12. 3/18/2016 Row Operations (Examples of Row-Echelon operation notation… …may be necessary for more than one operation) 3*R1 + R2 or 2*R1 + R2 5*R1 + R3 etc…

13. 3/18/2016 Row-Echelon Form A matrix is in row echelon form if: 1.Any rows consisting of entirely zeros occur at the bottom of the matrix 2.For each row that does not consist entirely of zeros, the first nonzero entry is a 1 3.As you work down the matrix the “leading 1” moves to the right. Still Makes the “Staircase”

14. 3/18/2016 Row-Echelon Form Row Echelon Form Not Row-Echelon Form

15. 3/18/2016 Row-Echelon Form A matrix is in reduced row echelon form if every entry above and below a leading 1 is 0.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. 3/18/2016 Row-Echelon Form You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

17. 3/18/20165.1a It’s the End of the Day: Do you know how to: Determine the Order of a matrix?Determine the Order of a matrix? Perform Elementary Row Operations?Perform Elementary Row Operations? Identify Elementary Row Operation?Identify Elementary Row Operation? Identify if a Matrix is in Row-Echelon Form?Identify if a Matrix is in Row-Echelon Form? Identify if a Matrix is in Reduced Row- Echelon Form?Identify if a Matrix is in Reduced Row- Echelon Form?

18. 3/18/2016Homework Study: INSERT HERE Do: Read & Take Notes: INSERT HERE

19. 3/18/2016 Resource Credits Justin Bohannon Justin Bohannon Justin Bohannon