# 2 2 r r r perform ero on r 1 so second column has 0

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Chapter 1 / Exercise 41
Mathematical Applications for the Management, Life, and Social Sciences
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Chapter 1 / Exercise 41
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger Expert Verified
Unit 5. Systems of Equations and Inequalities Section 3 page 10 _____________________________________________________________________________________ obtained, is called Gauss-Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (1842-1899).We have just learned to use matrices, Gaussian elimination,and Gauss-Jordan elimination to solve any system of linear equations. Coming up is yet another method that uses matrices for solving systems of linear equations; however, this can be used only when the number of equations is the same as the number of variables. Although this method can be used for any linear system satisfying this condition, here we will consider only systems with two equations and two variables or three equations and three variables. This method, called Cramer’s Rule, is based on the concept of a determinant. Every square matrix can be associated with a real number called its determinant.The Determinant of a 2 x 2 Matrix Keep This in Mind If a1, a2, b1, and b2are four real numbers, the determinantof the matrix 2211babaAis given by .12212211babababaAA diagram that may be helpful for remembering this formula for the determinant of a 2 x 2 matrix is the following: 12212211babababaA21ba12baTime to think! Solve the following system by Gauss-Jordan elimination: 07323322zyxzyxzyx
Unit 5. Systems of Equations and Inequalities Section 3 page 11 _____________________________________________________________________________________ Example 5.3.8 Determinant of a 2 x 2 matrix Find the determinant of each of the following matrices: 1.51810A2.1324BSolution:    428508151051810518101.AA   10642314132413242.BBNow let’s see the role that the determinant plays in the solution of a system of two linear equations in two variables.Theorem1: Cramer’s Rule for Two Linear Equations Containing Two VariablesGiven the system 222111cybxacybxawith 2211babaA, 2211bcbcAx, and 2211cacaAy, the solution to the linear system is given by AAxxand AAyyprovided that 0A.
Unit 5. Systems of Equations and Inequalities Section 3 page 12 _____________________________________________________________________________________
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