Linear Algebra Lecture 1: Introduction

Slides:

Advertisements

Similar presentations

Economics 214 Lecture 13 Systems of Equations. Examples of System of Equations Demand and Supply IS-LM Aggregate Demand and Supply.

Advertisements

Using Inverse Matrices Solving Systems. You can use the inverse of the coefficient matrix to find the solution. 3x + 2y = 7 4x - 5y = 11 Solve the system.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

Math 71A 3.1 – Systems of Linear Equations in Two Variables 1.

TODAY IN ALGEBRA…  Learning Goal: 7.2 You will solve systems of linear equations by Substitution  Independent Practice.

Determinants and Cramer’s Rule

Section 1.1 Introduction to Systems of Linear Equations.

1.1.2 INTRODUCTION TO SYSTEMS OF LINEAR EQUATIONS Chapter 1: Systems of Linear Equations and Matrices SWBAT: Redefine algebraic operations as Elementary.

College algebra 6.1 Systems of Linear Equations in Two Variables

4.5 Solving Systems using Matrix Equations and Inverses.

4.4 & 4.5 Notes Remember: Identity Matrices: If the product of two matrices equal the identity matrix then they are inverses.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.

Inverse Matrices and Systems

4-7 Inverse Matrices & Systems

1.3 The Intersection Point of Lines System of Equation A system of two equations in two variables looks like: – Notice, these are both lines. Linear Systems.

Do Now: Evaluate: 3AB. Algebra II 3.7: Evaluate Determinants HW: p.207 (4-14 even) Test : Friday, 12/6.

Find the determinant of this matrix Jeff buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buy 5 apples and 9 pears for $10.40.

Section 3.2 Connections to Algebra.  In algebra, you learned a system of two linear equations in x and y can have exactly one solution, no solutions,

Sullivan Algebra and Trigonometry: Section 12.3 Objectives of this Section Write the Augmented Matrix of a System of Linear Equations Write the System.

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.

1.4 Solving Multi-Step Equations. To isolate the variable, perform the inverse or opposite of every operation in the equation on both sides of the equation.

Complete the DO NOW in your packets

3.1 – Solve Linear Systems by Graphing A system of two linear equations in two variables x and y, also called a linear system, consists of two equations.

Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.

4.7 Solving Systems using Matrix Equations and Inverses

+ Unit 1 – First degree equations and inequalities Chapter 3 – Systems of Equation and Inequalities 3.1 – Solving Systems by Graphing.

Chapter 4: Systems of Equations and Inequalities Section 4.3: Solving Linear Systems Using Graphs.

SystemsOfInequalities. 7-1 Solving Systems by Graphing What is a system of linear equations? “SOLUTION” No solution Infinitely Many Solutions Page 342.

GUIDED PRACTICE for Example – – 2 12 – 4 – 6 A = Use a graphing calculator to find the inverse of the matrix A. Check the result by showing.

Warm up. Solving Systems Using Inverse Matrices Systems to Matrices A system of equations in standard form (Ax+By=C) can be written in matrix form [A][X]=[B]

Chapter 4 Section 5 and 6 Finding and Using Inverses Algebra 2 Notes February 26, 2009.

3.8B Solving Systems using Matrix Equations and Inverses.

Warm Up Multiply the matrices. 1. Find the determinant. 2. –1 Welcome! I’m so glad you’re here! Please get your Calculator. Please get started on this.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

Chapter 5: Matrices and Determinants Section 5.5: Augmented Matrix Solutions.

Warm Up 3(2x+3)= 7x x LIKE THIS ONE!!!!!

MTH108 Business Math I Lecture 20.

Use Inverse Matrices to Solve Linear Systems

Q1W5: Solving Linear Equations With One Variable

Linear Equations in One Variable

Algebra 1 Review Systems of Linear Equations Using Substitution

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

Matrix Addition and Scalar Multiplication

Matrix Multiplication

Review Problems Matrices

Chapter 7 – Systems of Linear Equations and Inequalities

6-2 Solving Systems using Substitution

Data Base System By: Nur Uddin, Ph.D.

Solving Linear Systems Algebraically

Section 6.4 Multiplicative Inverses of Matices and Matrix Equations

Solve Systems of Linear Equations in Three Variables

Use Inverse Matrices to Solve Linear Systems

Solving Linear Systems Using Inverse Matrices

Teori Bahasa dan Automata Lecture 1: Course Overview and Introduction

Multiplicative Inverses of Matrices and Matrix Equations

Use Inverse Matrices to Solve 2 Variable Linear Systems

Matrix Solutions to Linear Systems

Linear Algebra Lecture 3.

Inverse Matrices and Systems

Section 9.4 Multiplicative Inverses of Matices and Matrix Equations

4.4 Objectives Day 1: Find the determinants of 2  2 and 3  3 matrices. Day 2: Use Cramer’s rule to solve systems of linear equations. Vocabulary Determinant:

Study Daily- Substitution 4 question quiz-Friday

7.1 Solving Systems of Equations

Objective: Students will solve systems by graphing

Study Daily- Substitution 4 question quiz-Friday

Systems of three equations with three variables are often called 3-by-3 systems. In general, to find a single solution to any system of equations,

Solving Linear Systems of Equations - Inverse Matrix

Numerical Method Lecture 1: Introduction

Presentation transcript:

Linear Algebra Lecture 1: Introduction By: Nur Uddin, Ph.D

Lecturer Name: Nur Uddin, PhD. Email: nur.uddin@upj.ac.id Education: PhD in Eng. Cybernetics, NTNU, Norway (April 2016) M. Eng in Mechanical Eng., GSNU, South Korea (Feb 2009) B. Eng in Aeronautics Eng., ITB, Indonesia (Mar 2002)

Syllabus See in another file

Linear algebra in daily life

Example 1 Price of 3 apples is NOK 12. What is the prices of an apple? NOK: Norwegian Kroner

Example 2 Price of 3 bananas and 2 oranges is NOK 12. Price of 1 banana and 2 oranges is NOK 8. What are the prices of a banana and an orange?

Example 3 Price of 2 pears and 2 mangos is NOK 10. Price of 1 pear and 1 mango is NOK 5. What are the prices of a pear and a mango?

Linear equation

Linear equation system Linear equation system (linear system) is a collection of one or more linear equations involving the same variables

Solution A linear system may have: No solution One solution (exact solution) Infinite solutions

Solving Linear System: Example 1

Solving Linear System: Example 2

Solving Linear System: Example 3

Matrix

Matrices multiplication

Matrices representation

Matrices representation

Matrix representation

Matrix representation

Matrix representation

Solution using inverse matrix

Solution using inverse matrix

Homework