1 / 12

Lesson 12 – 5 Augmented Matrix

Lesson 12 – 5 Augmented Matrix. Pre-calculus Part 2 of 3. Learning Objective. To solve quadratic systems. Another way to solve a system of equations uses an augmented matrix. Augmented Matrix. In this method, we will create a “corner of zeros” and then let our algebra skills take over!.

suki
Download Presentation

Lesson 12 – 5 Augmented Matrix

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. Lesson 12 – 5 Augmented Matrix Pre-calculus Part 2 of 3

  2. Learning Objective • To solve quadratic systems

  3. Another way to solve a system of equations uses an augmented matrix. Augmented Matrix In this method, we will create a “corner of zeros” and then let our algebra skills take over! *A lot of math is done in our heads, so be careful! Also, write good instructions to yourself to follow.*

  4. 1. Solve the system using the augmented matrix method. Augmented Matrix  want 0 here –3R1 + R3 –2R1 + R2 0 here now 10R2 + (–9)R3 now 0 here

  5. Algebra takes over! Augmented Matrix If you are adept enough, you can try the first 2 steps at the same time to speed up the process. 

  6. Lesson 12 – 5 Augmented Matrix Pre-calculus Part 2 of 3

  7. 2. Solve the system using the augmented matrix method. Augmented Matrix  3R1 + (–2)R2 –2R1 + R3 2R2 + 13R3 

  8. Lesson 12 – 5 Augmented Matrix Pre-calculus Part 3 of 3

  9. An application is to find the equation of a circle (in general form) knowing 3 of its points Augmented Matrix 3. Determine the equation of the circle that passes through (2, 9), (8, 7), and (–8, –1) *Remember a circle in general form is For (2, 9): 4 + 81 + 2D + 9E + F = 0 For (8, 7): 64 + 49 + 8D + 7E + F = 0 For (–8, –1): 64 + 1 – 8D – E + F = 0

  10. Augmented Matrix  –4R1 + R2 R2 + R3 6R2 + 29R3

  11. Algebra takes over! Augmented Matrix

  12. Assignment Pg. 630 #1, 5, 11, 15, 17, 23, 27, 37

More Related