1 / 22

8.3 Matrices and Systems of Equations Day 1

8.3 Matrices and Systems of Equations Day 1. Do Now Solve the system of equations 2x – 3y = 7 x + 4y = -2. HW Review: 8.2 #1-23. Matrices and Systems. We can use an augmented matrix to represent systems of equations Ex: 2x – 3y = 7 x + 4y = -2. Matrices.

taniel
Download Presentation

8.3 Matrices and Systems of Equations Day 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 8.3 Matrices and Systems of EquationsDay 1 Do Now Solve the system of equations 2x – 3y = 7 x + 4y = -2

  2. HW Review: 8.2 #1-23

  3. Matrices and Systems • We can use an augmented matrix to represent systems of equations • Ex: 2x – 3y = 7 x + 4y = -2

  4. Matrices • The rows of a matrix are horizontal • The columns are vertical • A matrix with m rows and n columns is said to be of order m x n • The numbers in a matrix are called entries • The main diagonal starts from the top left and travels down and to the right

  5. Gaussian Elimination with Matrices • If we write a system of equations as an augmented matrix, we can use row-equivalent operations to write a matrix with a main diagonal of 1’s

  6. Row-Equivalent Operations • In a matrix, you are allowed to: • Interchange any two rows • Multiply each entry in a row by the same nonzero constant • Add a nonzero multiple of one row to another row

  7. Ex • Solve the system of equations 2x – y + 4z = -3 x – 2y – 10z = -6 3x + 4z = 7

  8. Ex • Solve the systems of equations using matrices x – y+ 2z = 0 x – 2y + 3z = -1 2x – 2y + z = -3

  9. Closure • Solve the system using matrices 4x – 8y = 12 -x + 2y = -3 • HW: p.710 #1-13 odds, 15-39 EOO

  10. 8.3 Matrices and SystemsDay 2 • Do Now • Solve the system using matrices 3x + 2y + 2z = 3 x + 2y – z = 5 2x – 4y + z = 0

  11. HW Review: p.710 #1-13, 15-39 EOO

  12. Row-Echelon Form • A matrix is in row-echelon form, then: • 1) The first nonzero element in each row is a 1 • 2) For any two successive nonzero rows, the leading 1 in the lower row is farther to the right than the leading 1 in the higher row • 3) All the rows consisting entirely of 0’s are at the bottom of the matrix • Note: a matrix is said to be in reduced row-echelon form if: • Each column that contains a leading 1 has 0’s everywhere else (except the last column of an augmented matrix)

  13. Ex • Ex2 on p.707 in book

  14. Gauss-Jordan Elimination • In this method, we want to write each system of equations as an augmented matrix in reduced row-echelon form

  15. Ex • Solve the system of equations 3x – 4y – z = 6 2x – y + z = -1 4x – 7y – 3z = 13

  16. Closure • Solve the system of equations 2x – 3y + 2z = 3 x + 4y – z = 9 3x + y – 5z = 5 • HW: p.710 #15-39 AOO

  17. 8.3 Matrices and SystemsDay 3 • Do Now • Solve the system of equations x + y – 3z = 4 4x + 5y + z = 1 2x + 3y + 7z = -7

  18. HW Review p.710 #15-39 AOO

  19. Closure • Would you rather use matrices or algebraic methods to solve a system of linear equations in 2/3 variables? Why? • 8.1-8.3 Quiz Friday

  20. 8.1-8.3 Review • Do Now • Solve the system of equations by any means x – y + z = 3 2x + y – 3z = 5 4x + y – z = 11

  21. 8.1-8.3 Review • 8.1 Solving Linear Systems in 2 variables • Graphing, Substitution, Elimination • 8.2 Solving Linear Systems in 3 Variables • Substitution or Elimination • 8.3 Using Matrices to Solve Systems • Elimination using Row-Equivalent Operations

  22. Closure • Solve this system of equations using as many methods as possible 2x + y = 1 3x + 2y = -2 8.1-8.3 Quiz Tomorrow

More Related