Dr. Mubashir Alam King Saud University. Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row.

Slides:

Advertisements

Similar presentations

4.1 Introduction to Matrices

Advertisements

Applied Informatics Štefan BEREŽNÝ

2. Review of Matrix Algebra Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical.

Section 1.7 Diagonal, Triangular, and Symmetric Matrices.

1.7 Diagonal, Triangular, and Symmetric Matrices.

Determinants (10/18/04) We learned previously the determinant of the 2 by 2 matrix A = is the number a d – b c. We need now to learn how to compute the.

Solution of Simultaneous Linear Algebraic Equations: Lecture (I)

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

Matrix Operations. Matrix Notation Example Equality of Matrices.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 14 Elimination Methods.

Chapter 2 Matrices Definition of a matrix.

ECIV 520 Structural Analysis II Review of Matrix Algebra.

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

Chapter 5 Determinants.

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

1.7 Diagonal, Triangular, and Symmetric Matrices 1.

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

Introduction The central problems of Linear Algebra are to study the properties of matrices and to investigate the solutions of systems of linear equations.

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

Dr. Mubashir Alam King Saud University. Outline Numerical Integration Trapezoidal and Simpson’s Rules (5.1)

ECON 1150 Matrix Operations Special Matrices

8.1 Vector spaces A set of vector is said to form a linear vector space V Chapter 8 Matrices and vector spaces.

Advanced Computer Graphics Spring 2014 K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology.

Presentation on Matrices and some special matrices In partial fulfillment of the subject Vector calculus and linear algebra ( ) Submitted by: Agarwal.

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.

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.

Determinants In this chapter we will study “determinants” or, more precisely, “determinant functions.” Unlike real-valued functions, such as f(x)=x 2,

Sec 3.5 Inverses of Matrices Where A is nxn Finding the inverse of A: Seq or row operations.

2.5 - Determinants & Multiplicative Inverses of Matrices.

1 MAC 2103 Module 3 Determinants. 2 Rev.F09 Learning Objectives Upon completing this module, you should be able to: 1. Determine the minor, cofactor,

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.

Co. Chapter 3 Determinants Linear Algebra. Ch03_2 Let A be an n  n matrix and c be a nonzero scalar. (a)If then |B| = …….. (b)If then |B| = …..... (c)If.

Chapter 3 Determinants Linear Algebra. Ch03_2 3.1 Introduction to Determinants Definition The determinant of a 2  2 matrix A is denoted |A| and is given.

4.4 Identify and Inverse Matrices Algebra 2. Learning Target I can find and use inverse matrix.

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.

Introduction and Definitions

MAT211 Lecture 17 Determinants.. Recall that a 2 x 2 matrix A is invertible If and only if a.d-b.c ≠ 0. The number a.d-b.c is the the determinant of A.

Dr. Mubashir Alam King Saud University. Outline LU Factorization (6.4) Solution by LU Factorization Compact Variants of Gaussian Elimination, (Doolittle’s.

Section 2.1 Determinants by Cofactor Expansion. THE DETERMINANT Recall from algebra, that the function f (x) = x 2 is a function from the real numbers.

REGRESSION (CONTINUED) Matrices & Matrix Algebra; Multivariate Regression LECTURE 5 Supplementary Readings: Wilks, chapters 6; Bevington, P.R., Robinson,

Matrices. Matrix - a rectangular array of variables or constants in horizontal rows and vertical columns enclosed in brackets. Element - each value in.

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

Matrices and systems of Equations. Definition of a Matrix * Rectangular array of real numbers m rows by n columns * Named using capital letters * First.

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

Characteristic Polynomial Hung-yi Lee. Outline Last lecture: Given eigenvalues, we know how to find eigenvectors or eigenspaces Check eigenvalues This.

Linear Algebra by Dr. Shorouk Ossama.

College Algebra Chapter 6 Matrices and Determinants and Applications

MTH108 Business Math I Lecture 20.

Matrices and Vector Concepts

Linear Algebraic Equations and Matrices

Introduction The central problems of Linear Algebra are to study the properties of matrices and to investigate the solutions of systems of linear equations.

Matrices and vector spaces

MATHEMATICS Linear Equations

Linear Algebraic Equations and Matrices

Linear independence and matrix rank

Linear Algebra Lecture 15.

DETERMINANT MATRIX YULVI ZAIKA.

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

Using Matrices to Solve Systems of Equations

Lecture 11 Matrices and Linear Algebra with MATLAB

CSE 541 – Numerical Methods

Fundamentals of Engineering Analysis

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

Elementary Linear Algebra Anton & Rorres, 9th Edition

Chapter 2 Determinants.

Presentation transcript:

Dr. Mubashir Alam King Saud University

Outline Systems of Linear Equations (6.1) Matrix Arithmetic (6.2) Arithmetic Operations (6.2.1) Elementary Row Operations (6.2.2) The Matrix Inverse (6.2.3) Matrix Algebra Rules (6.2.4) Solvability Theory of Linear Systems (6.2.5)

Matrix: (n x n) Known Vector: (n x 1) Known Vector: (n x 1) Unknown

Square Matrix m=n Elements of matrix

If and only if det(A)≠ 0

Special Matrices Diagonal Matrix Upper Triangular Matrix Lower Triangular Matrix Symmetric Matrix

R1-R2 R2-R3

R1-R2R3-2R1

Matrix Algebra Rules Covered on Textbook: Page:256