1 / 24

Determinants and Cramer’s Rule

Determinants and Cramer’s Rule. Determinants. Determinants. A real number A ssociated with square (n x n) matrices Determinant for Matrix A is denoted as det A or | A |. Finding the Determinant of a 2 x 2 Matrix:. Example 1: Find the determinant. Example 2: Find the determinant.

denise-malone
Télécharger la présentation

Determinants and Cramer’s Rule

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. Determinants and Cramer’s Rule

  2. Determinants

  3. Determinants • A real number • Associated with square (n x n) matrices • Determinant for Matrix A is denoted as det A or | A |

  4. Finding the Determinant of a 2 x 2 Matrix:

  5. Example 1: Find the determinant

  6. Example 2: Find the determinant

  7. Example 3: Find the determinant

  8. Practice 1: Find the determinant

  9. Cramer’s Rule

  10. Cramer’s Rule • Method for solving linear systems using matrices -Can be used to solve a linear system of any size *We will only be working with linear systems in two variables

  11. How to Solve Using Cramer’s Rule: • Create a coefficient matrix from the linear system ax + by = e cx + dy = f

  12. How to Solve Using Cramer’s Rule: • Create a coefficient matrix from the linear system ax + by = e cx + dy = f *Note that the coefficients for x are the first column and the coefficients for y are the second column

  13. How to Solve Using Cramer’s Rule: • Find the determinant of the coefficient matrix

  14. How to Solve Using Cramer’s Rule: • Find the determinant of the coefficient matrix *If det A ≠ 0, then there is exactly one solution

  15. How to Solve Using Cramer’s Rule: 3. Solve for x as follows: ax + by = e cx + dy = f

  16. How to Solve Using Cramer’s Rule: 3. Solve for x as follows: ax + by = e cx + dy = f *Note the coefficients for x have been replaced with the constants from the linear system

  17. How to Solve Using Cramer’s Rule: 4. Solve for y as follows: ax + by = e cx + dy = f

  18. How to Solve Using Cramer’s Rule: 4. Solve for y as follows: ax + by = e cx + dy = f *Note the coefficients for y have been replaced with the constants from the linear system

  19. How to Solve Using Cramer’s Rule: • Write the solution as a point (x,y)

  20. How to Solve Using Cramer’s Rule: • Write the solution as a point (x,y) 6. Check your solution by substituting the values into the original equation

  21. Example 1: Solve the following system using Cramer’s Rule: 2x + 7y = –3 3x – 8y = –23

  22. Example 2: Solve the following system using Cramer’s Rule: 4x + 12y = 11 14x – 8y = 1

  23. Practice 1: Solve the following system using Cramer’s Rule: 3x + 19y = 20 2x + 11y = 10

  24. Homework: Page 607 #1 – 15

More Related