Matrix Solutions to Linear Systems

Slides:

Advertisements

Similar presentations

International Studies Charter School

Advertisements

Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

Table of Contents Solving Linear Systems of Equations - Triangular Form Consider the following system of equations... The system is easily solved by starting.

Solving Systems of three equations with three variables Using substitution or elimination.

Gauss-Jordan Matrix Elimination Brought to you by Tutorial Services – The Math Center.

Table of Contents Solving Systems of Linear Equations - Gaussian Elimination The method of solving a linear system of equations by Gaussian Elimination.

7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.

8.1 Matrix Solutions to Linear Systems Veronica Fangzhu Xing 3 rd period.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

AN INTRODUCTION TO ELEMENTARY ROW OPERATIONS Tools to Solve Matrices.

1.1.2 INTRODUCTION TO SYSTEMS OF LINEAR EQUATIONS Chapter 1: Systems of Linear Equations and Matrices SWBAT: Redefine algebraic operations as Elementary.

Systems of Linear Equations Let’s say you need to solve the following for x, y, & z: 2x + y – 2z = 10 3x + 2y + 2z = 1 5x + 4y + 3z = 4 Two methods –Gaussian.

Guass-jordan Reduction :

College algebra 6.1 Systems of Linear Equations in Two Variables

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Chapter 6 Matrices and Determinants Copyright © 2014, 2010, 2007 Pearson Education, Inc Matrix Solutions to Linear Systems.

Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.

Solving Systems of 3 or More Variables Why a Matrix? In previous math classes you solved systems of two linear equations using the following method:

MCV4U1 Matrices and Gaussian Elimination Matrix: A rectangular array (Rows x Columns) of real numbers. Examples: (3 x 3 Matrix) (3 x 2 Matrix) (2 x 2 Matrix)

Matrices and Systems of Equations

Matrices and Systems of Linear Equations

Sullivan Algebra and Trigonometry: Section 12.3 Objectives of this Section Write the Augmented Matrix of a System of Linear Equations Write the System.

Class 7: Answers 1 (C) Which of the following matrices below is in reduced row echelon form? A B C D. None of them.

10.3 Systems of Linear Equations: Matrices. A matrix is defined as a rectangular array of numbers, Column 1Column 2 Column jColumn n Row 1 Row 2 Row 3.

10.2 Systems of Linear Equations: Matrices Objectives Objectives 1.Write the Augmented Matrix 2.Write the System from the Augmented matrix 3.Perform Row.

Matrices and Systems of Equations

Meeting 19 System of Linear Equations. Linear Equations A solution of a linear equation in n variables is a sequence of n real numbers s 1, s 2,..., s.

Section 5.3 Solving Systems of Equations Using the Elimination Method There are two methods to solve systems of equations: The Substitution Method The.

1 Section 5.3 Linear Systems of Equations. 2 THREE EQUATIONS WITH THREE VARIABLES Consider the linear system of three equations below with three unknowns.

Elimination Method: Solve the linear system. -8x + 3y=12 8x - 9y=12.

3.6 Solving Systems Using Matrices You can use a matrix to represent and solve a system of equations without writing the variables. A matrix is a rectangular.

7.3 & 7.4 – MATRICES AND SYSTEMS OF EQUATIONS. I N THIS SECTION, YOU WILL LEARN TO  Write a matrix and identify its order  Perform elementary row operations.

Solving Linear Systems by Substitution

RECOGNIZING INCONSISTENT LINEAR SYSTEMS. What is an Inconsistent Linear System?  An inconsistent linear system is a system of equations that has no solutions.

 Recall that when you wanted to solve a system of equations, you used to use two different methods.  Substitution Method  Addition Method.

Chapter 6 Matrices and Determinants Copyright © 2014, 2010, 2007 Pearson Education, Inc Inconsistent and Dependent Systems and Their Applications.

Chapter 8 Systems of Linear Equations in Two Variables Section 8.3.

SYSTEMS OF LINEAR EQUATIONS College Algebra. Graphing and Substitution Solving a system by graphing Types of systems Solving by substitution Applications.

Chapter 5: Matrices and Determinants Section 5.5: Augmented Matrix Solutions.

College Algebra Chapter 6 Matrices and Determinants and Applications

Downhill product – Uphill product.

Multivariable Linear Systems and Row Operations

TYPES OF SOLUTIONS SOLVING EQUATIONS

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Systems of linear equations

Gaussian Elimination and Gauss-Jordan Elimination

Systems of Linear Equations: Matrices

TYPES OF SOLUTIONS SOLVING EQUATIONS

Chapter 12 Section 1.

1.6 Further Results on Systems

Systems of Linear Equations

6-2 Solving Systems using Substitution

Chapter 6 Direct Methods for Solving Linear Systems

Choose the matrix in echelon form from the following:

Solving Linear Systems Algebraically

Solve a system of linear equation in two variables

Inconsistent and Dependent Systems and Their Applications

Systems of Linear Equations in Two Variables

Larger Systems of Linear Equations and Matrices

Chapter 4 Systems of Linear Equations; Matrices

Warm-up: Find the equation of the parabola y = ax2 + bx + c that passes through the given points: (-1, 4), (1, -6), (2, -5) CW: 7.1 – 7.3 Systems Quiz.

8.1 Matrices and System of Linear Equations

Gaussian Elimination.

College Algebra Chapter 6 Matrices and Determinants and Applications

Systems of Equations Solve by Graphing.

Solve the linear system.

Chapter 4 Systems of Linear Equations; Matrices

Warm-up: Solve the system by any method:

Multivariable Linear Systems

Example 2B: Solving Linear Systems by Elimination

Presentation transcript:

Matrix Solutions to Linear Systems

1. Write the augmented matrix for each system of linear equations (similar to p.564 #2)

2. Write the augmented matrix for each system of linear equations (similar to p.564 #6)

3. Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z for the variables (similar to p.564 #10)

4. Do the indicated row operation (similar to p.565 #14)

5. Do the indicated row operation (similar to p.565 #16)

6. Solve each system of equations using matrices 6. Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination (similar to p.565 #26)

7. Solve each system of equations using matrices 7. Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination (similar to p.565 #36)