Matrix Operations. Matrix Notation Example Equality of Matrices.

Slides:

Advertisements

Similar presentations

Section 1.7 Diagonal, Triangular, and Symmetric Matrices.

Advertisements

Matrix Definition: An array of numbers in m rows and n colums is called an mxn matrix A square matrix of order n, is an (nxn) matrix.

Matrices & Systems of Linear Equations

3_3 An Useful Overview of Matrix Algebra

Maths for Computer Graphics

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 12 System of Linear Equations.

Chapter 2 Matrices Definition of a matrix.

Part 3 Chapter 8 Linear Algebraic Equations and Matrices PowerPoints organized by Dr. Michael R. Gustafson II, Duke University All images copyright © The.

Arithmetic Operations on Matrices. 1. Definition of Matrix 2. Column, Row and Square Matrix 3. Addition and Subtraction of Matrices 4. Multiplying Row.

CE 311 K - Introduction to Computer Methods Daene C. McKinney

A matrix having a single row is called a row matrix. e.g.,

Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 1.

Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 1.

CHAPTER 2 MATRIX. CHAPTER OUTLINE 2.1 Introduction 2.2 Types of Matrices 2.3 Determinants 2.4 The Inverse of a Square Matrix 2.5 Types of Solutions to.

Review of Matrices Or A Fast Introduction.

Overview Definitions Basic matrix operations (+, -, x) Determinants and inverses.

10.4 Matrix Algebra 1.Matrix Notation 2.Sum/Difference of 2 matrices 3.Scalar multiple 4.Product of 2 matrices 5.Identity Matrix 6.Inverse of a matrix.

Algebra 3: Section 5.5 Objectives of this Section Find the Sum and Difference of Two Matrices Find Scalar Multiples of a Matrix Find the Product of Two.

Chapter 4 Section 4: Inverse and Identity Matrices 1.

CHAPTER 2 MATRICES 2.1 Operations with Matrices Matrix

Linear Algebra 1.Basic concepts 2.Matrix operations.

Linear algebra: matrix Eigen-value Problems Eng. Hassan S. Migdadi Part 1.

Chapter 6 Systems of Linear Equations and Matrices Sections 6.3 – 6.5.

Meeting 18 Matrix Operations. Matrix If A is an m x n matrix - that is, a matrix with m rows and n columns – then the scalar entry in the i th row and.

CSCI 171 Presentation 9 Matrix Theory. Matrix – Rectangular array –i th row, j th column, i,j element –Square matrix, diagonal –Diagonal matrix –Equality.

Chapter 2 Determinants. With each square matrix it is possible to associate a real number called the determinant of the matrix. The value of this number.

10.4 Matrix Algebra 1.Matrix Notation 2.Sum/Difference of 2 matrices 3.Scalar multiple 4.Product of 2 matrices 5.Identity Matrix 6.Inverse of a matrix.

MATRICES Operations with Matrices Properties of Matrix Operations

1.7 Linear Independence. in R n is said to be linearly independent if has only the trivial solution. in R n is said to be linearly dependent if there.

MATRIX A set of numbers arranged in rows and columns enclosed in round or square brackets is called a matrix. The order of a matrix gives the number of.

STROUD Worked examples and exercises are in the text Programme 5: Matrices MATRICES PROGRAMME 5.

2.5 – Determinants and Multiplicative Inverses of Matrices.

LEARNING OUTCOMES At the end of this topic, student should be able to :  D efination of matrix  Identify the different types of matrices such as rectangular,

Linear System of Simultaneous Equations Warm UP First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct:

2 - 1 Chapter 2A Matrices 2A.1 Definition, and Operations of Matrices: 1 Sums and Scalar Products; 2 Matrix Multiplication 2A.2 Properties of Matrix Operations;

Linear Algebra Engineering Mathematics-I. Linear Systems in Two Unknowns Engineering Mathematics-I.

§9-3 Matrix Operations. Matrix Notation The matrix has 2 rows and 3 columns.

Matrices. Variety of engineering problems lead to the need to solve systems of linear equations matrixcolumn vectors.

Introduction Types of Matrices Operations

Section 6-2: Matrix Multiplication, Inverses and Determinants There are three basic matrix operations. 1.Matrix Addition 2.Scalar Multiplication 3.Matrix.

10.4 Matrix Algebra. 1. Matrix Notation A matrix is an array of numbers. Definition Definition: The Dimension of a matrix is m x n “m by n” where m =

2.1 Matrix Operations 2. Matrix Algebra. j -th column i -th row Diagonal entries Diagonal matrix : a square matrix whose nondiagonal entries are zero.

1 Matrix Math ©Anthony Steed Overview n To revise Vectors Matrices.

CHAPTER 7 Determinant s. Outline - Permutation - Definition of the Determinant - Properties of Determinants - Evaluation of Determinants by Elementary.

1.4 The Matrix Equation Ax = b

College Algebra Chapter 6 Matrices and Determinants and Applications

MTH108 Business Math I Lecture 20.

Matrices and Vector Concepts

Linear Algebraic Equations and Matrices

Linear Algebra Lecture 2.

Unit 1: Matrices Day 1 Aug. 7th, 2012.

Linear Algebraic Equations and Matrices

Multiplication of Matrices

Matrix Operations SpringSemester 2017.

Section 1.8: Introduction to Linear Transformations.

الوحدة السابعة : المصفوفات . تنظيم البيانات فى مصفوفات . الوحدة السابعة : المصفوفات . تنظيم البيانات فى مصفوفات . 1 جمع المصفوفات وطرحها.

Vectors, Linear Combinations and Linear Independence

RECORD. RECORD Gaussian Elimination: derived system back-substitution.

2. Matrix Algebra 2.1 Matrix Operations.

Lecture 11 Matrices and Linear Algebra with MATLAB

Unit 3: Matrices

1.3 Vector Equations.

RECORD. RECORD COLLABORATE: Discuss: Is the statement below correct? Try a 2x2 example.

Determinant of a Matrix

MATRICES Operations with Matrices Properties of Matrix Operations

Matrix Definitions It is assumed you are already familiar with the terms matrix, matrix transpose, vector, row vector, column vector, unit vector, zero.

Multiplication of Matrices

Matrix Operations SpringSemester 2017.

L4-5/L4-6 Objective: Students will be able to evaluate determinants of matrices.

Presentation transcript:

Matrix Operations

Matrix Notation

Example

Equality of Matrices

Square Matrix

Diagonal Matrix

Triangular Matrices

Row and Column Vectors

Transposition of Vectors

Transposition of Matrices

Example

Symmetric and Skew-Symmetric Matrices

Addition of Matrices

Scalar Multiplication

Zero Matrix

Properties of Additon

Properties of Scalar Multiplication

Properties of Tranposition

Product of Matricies

Identity Matrices

Identity Property

A System of Linear Equations

The Matrix Equation Ax=b

Properties of Matrix Multiplication

Cautions

Matrix Powers

Theorem

Properties of Transposition

Definition of Linear Combination

Consistency Theorem for Linear Systems A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.

Definition

Matrix Inverse Identities