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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!.

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Lesson 12 – 5 Augmented Matrix

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  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

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