Chapter 8 By Briana, Brandon, Kyle, and Michaela

Vocab Matrix Augmented Matrix Coefficient Matrix Scalar Multiplication Reduced Row Echelon Form Gauss-Jordan Elimination Inverse Matrix Determinant Cramer's Rule

Concepts/Formulas Gauss-Jordan Elimination: uses augmented matrices to solve systems of linear equations Without a Calculator: 1.Write system as Augmented Matrix 2. Using row operations work down, around, and up to obtain RREF (see number 4) With a Calculator: 1.Hit 2 nd then matrix 2. Arrow over to edit and hit enter then put in the dimensions 3. Hit 2 nd quit and then hit 2 nd matrix and arrow over to math 4. Go to letter B( which is rref) 5. Hit 2 nd matrix and click enter on the desired one (see number 6)

Concepts/Formulas cont… Inverse Matrices: Inverse with Calculator: 1.Enter the matrix into the calculator 2. hit matrix then A then enter and then x -1 Uses: Used to solve a coefficient matrix equation (see number 5)

Concepts/Formulas cont… Determinant: (See number 3) With Calculator: 1.Hit 2 nd matrix and enter the dimensions 2. Hit 2 nd matrix and arrow over to math and click 1 and hit enter. 3.Click second and pick the matrix you want. Cramer’s Rule: (see number 8&9)

Concepts/Formulas cont… Triangle area: Test for Collinear Points: 3 points are collinear if and only if:

Problem Set 1. What is the order of this matrix? Find the value of 4. Solve the system using Gauss-Jordan Elimination 5x+4y=2 -x+y= Find the Inverse, if it exists, of 6. Solve using Gauss-Jordan Elimination using calculator

7. Write the original augmented matrix to solve the system. 8. Solve this system using Cramer's Rule. 9. Solve using Cramer's Rule. 10. A corporation has 4 factories, each of which manufactures 3 types of cordless power tools. The number of cordless power tools produced at each factory in one day is represented by each entry in this matrix. Find the production levels if the production is decreased by 5%