'Row echelon' presentation slideshows

Chapter 7

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Splash Screen

Splash Screen. Five-Minute Check (over Lesson 6-1) Then/Now New Vocabulary Key Concept: Matrix Multiplication Example 1: Multiply Matrices Key Concept: Properties of Matrix Multiplication Example 2: Real-World Example: Multiply Matrices Key Concept: Identity Matrix

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Lecture 9 Vector & Inner Product Spaces

Lecture 9 Vector & Inner Product Spaces. Last Time Spanning Sets and Linear Independence (Cont.) Basis and Dimension Rank of a Matrix and Systems of Linear Equations. Elementary Linear Algebra R. Larsen et al. (6th Edition) TKUEE ??? -NTUEE SCC_12_2008.

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Lesson 8 Gauss Jordan Elimination

Lesson 8 Gauss Jordan Elimination. Serial and Parallel algorithms. Linear Systems. A finite set of linear equations in the variables is called a system of linear equations or a linear system . A sequence of numbers

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Chapter 4 Systems of Linear Equations; Matrices

Chapter 4 Systems of Linear Equations; Matrices. Section 3 Gauss-Jordan Elimination. Gauss-Jordan Elimination . Any linear system must have exactly one solution , no solution , or an infinite number of solutions .

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College algebra

College algebra . 6.1 Systems of Linear Equations in Two Variables 6.2 Systems of Equations in Three Variables 6.3 Nonlinear Systems of Equations 7.1 Gaussian Elimination Method 7.2 Algebra of Matrices. 6.1 Systems of Equations in Two Variables.

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5.2 Rank of a Matrix

5.2 Rank of a Matrix. Set-up. Recall block multiplication:. Theorem 1. The following conditions are equivalent for an n x n matrix A: 1. The rows of A are linearly independent in ? n . 2. The rows of A span ? n . 3. The columns of A are linearly independent in ? n .

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Introduction to System of Linear Equations Gaussian Elimination Matrices and Matrix Operations

Chapter 1 Systems of Linear Equations and Matrices. Introduction to System of Linear Equations Gaussian Elimination Matrices and Matrix Operations Inverses; Rules of Matrix Arithmetic Elementary Matrices and a Method for Finding Further Results on Systems of Equations and Invertibility

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Introduction to System of Linear Equations Gaussian Elimination Matrices and Matrix Operations

Chapter 1 Systems of Linear Equations and Matrices. Introduction to System of Linear Equations Gaussian Elimination Matrices and Matrix Operations Inverses; Rules of Matrix Arithmetic Elementary Matrices and a Method for Finding Further Results on Systems of Equations and Invertibility

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Linear Transformations

Linear Transformations. Fall 2009. Definitions. Let V and W be vector spaces. A function L:V ? W is called a linear transformation of V into W if a) L( u + v ) = L( u ) + L( v ) b) L( c u ) = c L( u ) for u ? V and real c If V = W, then L is called a linear operator.

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Multivariate Linear Systems and Row Operations

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Chapter 8 Matrices and Determinants

Chapter 8 Matrices and Determinants. By Richard Warner, Nate Huyser , Anastasia Sanderson, Bailey Grote. Chapter 8.1: General Matrices. Rectangular array of numbers called entries Dimensions of a matrix are number of rows by the number of columns. Chapter 8.1: Augmented Matrices.

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1.2 Gaussian Elimination

1.2 Gaussian Elimination. Row-Echelon Form. In 1.1, we worked on manipulating an augmented matrix using elementary row operations so that our resulting equations could easily be solved for the values of the variables. Our Goal was to get the augmented matrix into Row-Echelon Form:

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Systems with Three Variables

Systems with Three Variables. Objective: I can solve systems with three or more variables. How much does each box weigh? Explain your reasoning. Solve the system. Solve the system. You manage a clothing store and budget $6000 to restock 200 shirts.

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7.3 Multivariable Linear Systems

7.3 Multivariable Linear Systems. We will be looking at equations with 3 variables like Equations generate a plane in the x-y-z coordinate plane. Graph using the intercepts (when the other variables are 0). (0, 0, 3). (0, 6, 0). (4, 0, 0). Types of Solutions 2 variable systems:.

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7.3 Multivariable Systems

7.3 Multivariable Systems. Row-echelon form. Solve the following system that is in row-echelon form. Answer. Start at the bottom because it is already solved for the variable. Gaussian Elimination. Row operations-transform system into equivalent system 1. Interchange 2 equations

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Multivariate Linear Systems and Row Operations

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Guass-jordan Reduction :

Guass-jordan Reduction :. Step 1 : Form the augmented matrix corresponding to the system of linear equations. Step 2 : Transform the augmented matrix to the matrix in reduced row echelon form by using elementary row operations.

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7.4C Gauss-Jordan Elimination

7.4C Gauss-Jordan Elimination. Guass -Jordan Elimination : Creates a matrix in REDUCED ROW ECHELON FORM . (Use row operations) Row Echelon form Rows with all zeros are at bottom First non-zero entry in each row is a 1

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7.4 Matrices-Gauss-Jordan

7.4 Matrices-Gauss-Jordan. Gauss-Jordan elimination. Transform matrix into reduced row-echelon form. Gauss-Jordan. Solve. Answer. Transform into reduced row echelon form. Gauss-Jordan. Solve. Answer. Transform into reduced row echelon form.

240 views • 6 slides