'Elementary row operations' diaporamas de présentation

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INDR 262 INTRODUCTION TO O PTIMIZATION METHODS

INDR 262 INTRODUCTION TO O PTIMIZATION METHODS. LINEAR ALGEBRA. Matrices. m and n are positive integers Order of matrix : m x n The number in the i th row and j th column of A is called the ij th element of A and is written a ij . Example. Equal Matrices .

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More on Inverse

More on Inverse. Last Week Review. Matrix Rule of addition Rule of multiplication Transpose Main Diagonal Dot Product Block Multiplication. Matrix and Linear Equations Basic Solution X 1 + X 0 Linear Combination All solutions of LES Inverse Det Matrix Inversion Method

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Chapter 1 Introduction to Linear systems and Matrices

Chapter 1 Introduction to Linear systems and Matrices. 1.1 Introduction. A general linear system of m equations in n unknowns looks like. A system with at least one solution is called consistent , a system with no solution at all is called inconsistent .

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Simplex method (algebraic interpretation)

Simplex method (algebraic interpretation). Add slack variables( ???? ) to each constraint to convert them to equations. (We may refer it as an augmented LP). (1). (2).

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Fundamentals of Engineering Analysis

Gaussian Elimination Part B . Fundamentals of Engineering Analysis . Eng. Hassan S. Migdadi. Matrices and Row Operations. column. rows. row . columns. A matrix is a rectangular array of numbers. We subscript entries to tell their location in the array.

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Learning Objectives

Learning Objectives. Three Domains of Learning Objectives Cognitive Domain Affective Domain Motor-Skills Domain. Learning Objectives. Three Domains of Learning Objectives Cognitive Domain

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Hawkes Learning Systems College Algebra

Hawkes Learning Systems College Algebra. Section 8.2: Matrix Notation and Gaussian Elimination. Objectives. Linear systems, matrices, and augmented matrices. Gaussian elimination and row echelon form. Gauss-Jordan elimination and reduced row echelon form. Linear Systems and Matrices.

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row

column. rows. row. columns. Matrices. A matrix is a rectangular array of numbers. We subscript entries to tell their location in the array. Matrices are identified by their size. main diagonal. A matrix that has the same number of rows as columns is called a square matrix.

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Linear Systems

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Multivariate Linear Systems and Row Operations

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Section 2.1

Section 2.1 . Solving System of Linear Equations. 2.1 Solving Systems of Linear Equations I. Diagonal Form of a System of Equations Elementary Row Operations Elementary Row Operation 1 Elementary Row Operation 2 Elementary Row Operation 3 Gaussian Elimination Method

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Chapter 1

Chapter 1. Section 5. Elementary Matrices. An elementary matrix of type I is a matrix obtained by interchanging two rows of I. Elementary Matrices. R ow 1 and Row 2 are switched!. C olumn 1 and Column 2 are switched!. Elementary Matrices.

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Examples

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Chapter 1 Systems of Linear Equations

Chapter 1 Systems of Linear Equations. A. B. i.e.,. Summary. Use row operations to [ A : B ] :. Def. [ I n : X ] is called the reduced echelon form of [ A : B ].

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Simplex Method

Simplex Method. LP problem in standard form. Canonical (slack) form. : basic variables : nonbasic variables. Some definitions. basic solution solution obtained from canonical system by setting nonbasic variables to zero

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Multivariate Linear Systems and Row Operations

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Chapter 1

Chapter 1. Section 1. Examples:. 2 x 2 system. 2 x 3 system. 3 x 2 system. The order in which any two equations are written may be interchanged System 1: System 2: (x 1 ,x 2 ,x 3 ) is a solution to System 1 if any only if it is a solution to to System 2.

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Chapter 1

Chapter 1. Section 1.1 Introduction to Matrices and systems of Linear Equations. Larger Systems of Equations A system of equations that has 3 or more variables can be solved by combining both the elimination method and the substitution method.

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2.5 The Gauss-Jordan Method for Calculating Inverses

2.5 The Gauss-Jordan Method for Calculating Inverses. Gauss-Jordan Method for Inverses. Gauss-Jordan Method for Inverses. Step 1: Write down the matrix A , and on its right write an identity matrix of the same size.

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