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Multivariate Linear Systems and Row Operations

Precalculus. Lesson 7.3 Part 2. Multivariate Linear Systems and Row Operations. Quick Review. ?. Yes. What you’ll learn about. Triangular Forms for Linear Systems Gaussian Elimination Elementary Row Operations and Row Echelon Form Reduced Row Echelon Form

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Multivariate Linear Systems and Row Operations

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  1. Precalculus Lesson 7.3 Part 2 Multivariate Linear Systems and Row Operations

  2. Quick Review ? Yes

  3. What you’ll learn about • Triangular Forms for Linear Systems • Gaussian Elimination • Elementary Row Operations and Row Echelon Form • Reduced Row Echelon Form • Solving Systems with Inverse Matrices • Applications … and why Many applications in business and science are modeled by systems of linear equations in three or more variables.

  4. Example Solving a System Using Inverse Matrices

  5. Example Solving a System Using Inverse Matrices

  6. Example Application Problem Stewart’s Metals has three silver alloys on hand. One is 22% silver, another is 30% silver, and the third is 42% silver. How many grams of each alloy is required to produce 80 grams of a new alloy that is 34% silver if the amount of 30% alloy is used twice the amount of 22% alloy used?

  7. Example Application Problem Stewart’s Metals has three silver alloys on hand. One is 22% silver, another is 30% silver, and the third is 42% silver. How many grams of each alloy is required to produce 80 grams of a new alloy that is 34% silver if the amount of 30% alloy is used twice the amount of 22% alloy used?

  8. Example Application Problem Stewart’s Metals has three silver alloys on hand. One is 22% silver, another is 30% silver, and the third is 42% silver. How many grams of each alloy is required to produce 80 grams of a new alloy that is 34% silver if the amount of 30% alloy is used twice the amount of 22% alloy used? Therefore, is about 14.55 grams of the 22% silver, 29.09 grams of the 30% silver, and 36.36 grams of the 42% silver is needed.

  9. Homework: Text pg603/604 Exercises #43,45,47,49,79

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