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**Unformatted text preview: **Linear Algebra Math1111 Linear Algebra MATH1111 Linear Algebra ( MATH1111 ) Instructor: Dr. Y.K. Lau http://147.8.101.93/MATH1111/ Linear Algebra Math1111 Applications of Linear Algebra Examples Economics : Input-output analysis.- Invented by Wassily Leontief- Awarded the Nobel prize in 1973 (Leontief, 1906-1999) Linear Algebra Math1111 Applications of Linear Algebra Examples Economics : Input-output analysis.- Invented by Wassily Leontief- Awarded the Nobel prize in 1973 (Leontief, 1906-1999) Search engine : Google- Invented by two Standford graduate students: Sergey Brin & Larry Page- Founded Google Inc. (Page, 1973-) (Brin, 1973- ) Linear Algebra Math1111 Linear Algebra & other subjects What branches/subjects will apply notions or techniques in linear algebra?- Differential equations, Operations research, Probability theory, Functional analysis, ....- Linear regression, Logistics, Time series, Forecasting, .... Mechanics, Coding theory, Econometric, Risk theory, .... Bioinformatic, Data mining, .... Follow-up courses : Matrix theory and its applications (MATH2304) Linear Algebra Math1111 What’s Linear Algebra? • What is linear algebra? Naively, linear algebra = linear + algebra Linear Algebra Math1111 What’s Linear Algebra? • What is linear algebra? Naively, linear algebra = linear + algebra • Linear - concern with straight lines or its properties. • Algebra - "a branch of mathematics concerning the study of of structure, relation and quantity" [Wikipedia] Linear Algebra Math1111 What’s Linear Algebra? • What is linear algebra? Naively, linear algebra = linear + algebra • Linear - concern with straight lines or its properties. • Algebra - "a branch of mathematics concerning the study of of structure, relation and quantity" [Wikipedia] • Linear algebra - a subject to study the structure, relation, etc, of "linear things". Linear Algebra Math1111 What’s Linear Algebra? • What is linear algebra? Naively, linear algebra = linear + algebra • Linear - concern with straight lines or its properties. • Algebra - "a branch of mathematics concerning the study of of structure, relation and quantity" [Wikipedia] • Linear algebra - a subject to study the structure, relation, etc, of "linear things". • What are linear things? Examples: x + 2 y = 3 , x + y- z = 4 , ··· Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Objectives Question What are we going to study? Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Objectives Question What are we going to study? Let us illustrate with simple examples: (a) x 1 + x 2 = 2 x 1- x 2 = 2 (b) x 1 + x 2 = 2 x 1 + x 2 = 1 (c) x 1 + x 2 = 2- x 1- x 2 =- 2 Chapter 1. Matrices and Systems of Equations Math1111 Systems of Linear Equations Objectives Question What are we going to study?...

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