Chapter 8 Study Guide

Example 5: Writing the Augmented Matrix of a System of Linear Equations 7.Write the augmented matrix of the given system of equations

2x+3y-6=0 4x-6y+2=0

Example 7: An Inconsistent System of Equations 25.Solve each system of equations. If inconsistent, say no solution.

2x+y=1 4x+2y=3

Example 5: How to Solve a System of Linear Equations by Elimination 27.Solve each system of equations. If inconsistent, say no solution.

2x-y=0 4x+2y=12

Example 5: Operations Using Matrices 13.Use the following matrices to evaluate the given expression. A=|0 3 -5| B=|4 1 0| C=|4 1| |1 2 6| |-2 3 -2| |6 2| |-2 3|

3A-2B

Example 2: Examples of Systems of Equations 9.Verify that the values of the variables listed are solutions of the system of equations?

3x-4y=5 1/2x--3y=-1/2 x=2, y=1/2; (2,1/2)

Example 4: How to Solve a System of Linear Equations by Substitution 19.Solve each system of equations. If inconsistent, say no solution.

5x-y=21 2x+3y=-12

Example 15: Using the Inverse Matrix to Solve a System of Linear Equations 45.Use the inverse in Problem 33 to solve each system of equations.

6x+5y=7 2x+2y=2

Example 3: Adding and Subtracting Matrices 9.Use the following matrices to evaluate the given expression. A=|0 3 -5| B=|4 1 0| C=|4 1| |1 2 6| |-2 3 -2| |6 2| |-2 3|

A+B

Example 9:Multiplying Two Matrices 15.Use the following matrices to evaluate the given expression. A=|0 3 -5| B=|4 1 0| C=|4 1| |1 2 6| |-2 3 -2| |6 2| |-2 3|

AC

Example 9:Multiplying Two Matrices 17.Use the following matrices to evaluate the given expression. A=|0 3 -5| B=|4 1 0| C=|4 1| |1 2 6| |-2 3 -2| |6 2| |-2 3|

CA

Example 5: Using Cramer's Rule 33.Solve each system of equations using Cramer's Rule if it is applicable

x+ y - z=6 3x-2y+ z=-5 x+3y-2z=14

Example 7: An Inconsistent System of Equations 29.Solve each system of equations. If inconsistent, say no solution.

x+2y=4 2x+4y=8

Example 2: Solving a System of Linear Equations Using Determinants 15.Solve each system of equations using Cramer's Rule if it is applicable

x+y=8 x-y=4

Example 6: Solving a System of Linear Equations Using Matrices(Row Echelon Form) 37. Solve each system of equations using matrices(row operations)

x+y=8 x-y=4

Example 11: Solving a System of Dependent Equations 45.Solve each system of equations. If inconsistent, say no solution.

x- y-z=1 2x+3y+z=2 3x+2y =0

Example 9: Solving a System of Three Linear Equations with Three Variables 43.Solve each system of equations. If inconsistent, say no solution.

x-2y+3z=7 2x+y+ z=4 -3x+2y-2z=-10

Example 6: Solving a System of Linear Equations Using Matrices(Row Echelon Form) 47. Solve each system of equations using matrices(row operations)

x-y =6 2x -3z=16 2y+ z=4

Example 2: Solving a System of Nonlinear Equations Using Eliminations 13.

x^2 + y^2 = 4 x^2 + 2x + y^2 =0

Example 1: Solving a System of Nonlinear Equations Using Substitution 15. Solve the system to find the points of intersection

y =3x-5 x^2 + y^2 =5

Example 3: Finding Minors of a 3 by 3 Determinant 9. Find the minors of the determinant

|-3 -1| |4 2|

Example 8: Multiplying Two Matrices 25.Find the Product

|2 -2| |2 1 4 6| |1 0| |3 -1 3 2|

Example 4: Evaluating a 3x3 Determinant 11. Find the value of each determinant

|3 4 2| |1 -1 5| |1 2 -2|

Example 1: Evaluating a 2x2 Determinant 7. Find the value of each determinant.

|6 4| |-1 3|

Example 13: Finding the Inverse of a Matrix 33.Find the inverse of each matrix

|6 5| |2 2|