Notes Over 10.5 Using Cramer’s Rule for a 2 x 2 System

Slides:

Advertisements

Similar presentations

TRIVIA Click for Question What kind of matrix contains the coefficients and constants of a system of linear equations? An augmented matrix Click for:

Advertisements

4-5 Matrix Inverses and Solving Systems Warm Up Lesson Presentation

MATRICES Using matrices to solve Systems of Equations.

Using Matrices to Solve a 3-Variable System

Copyright © Cengage Learning. All rights reserved. 7.8 Applications of Matrices and Determinants.

4-6 3x3 Matrices, Determinants, & Inverses

Gabriel Cramer was a Swiss mathematician ( )

AN INTRODUCTION TO ELEMENTARY ROW OPERATIONS Tools to Solve Matrices.

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.

4.5 Solving Systems using Matrix Equations and Inverses.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

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

Chapter 8 By Briana, Brandon, Kyle, and Michaela.

4.5 Solving Systems using Matrix Equations and Inverses OBJ: To solve systems of linear equations using inverse matrices & use systems of linear equations.

4-8 Augmented Matrices and Systems

4.6 Cramer’s Rule Using Determinants to solve systems of equations.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 9 Matrices and Determinants.

Holt Algebra Matrix Inverses and Solving Systems A matrix can have an inverse only if it is a square matrix. But not all square matrices have inverses.

Chapter 9 Matrices and Determinants Copyright © 2014, 2010, 2007 Pearson Education, Inc Multiplicative Inverses of Matrices and Matrix Equations.

Using Inverse Matrices in Real Life

What you will learn 1. What an identity matrix is

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Row Operations Matrix Operations.

4.3 Determinants and Cramer’s rule How do you find the determinant of a matrix? How do you find the area of a triangle given 3 sets of coordinates? How.

4.4 Identity and Inverse Matrices

Matrices and Systems of Linear Equations

Cramer’s Rule for Matrices You can use properties of matrix determinants for a variety of applications. Today: – Solving 3 variable systems of equations.

4-8 Augmented Matrices & Systems. Objectives Solving Systems Using Cramer’s Rule Solving Systems Using Augmented Matrices.

Copyright © Cengage Learning. All rights reserved. 7 Linear Systems and Matrices.

4.7 Solving Systems using Matrix Equations and Inverses

4-8 Cramer’s Rule We can solve a system of linear equations that has a unique solution by using determinants and a pattern called Cramer’s Rule (named.

Chapter Seven Linear Systems and Matrices 7.7 Determinants 7.8 Applications of Determinants.

Notes Over 4.4 Finding the Inverse of 2 x 2 Matrix.

Warm Up Determine whether each system has zero, one or infinitely many solutions one infinitely many zero 3x + y = 15 3x – 2y = 6 x + 2y = 18.

Determinants Every n  n matrix A is associated with a real number called the determinant of A, written  A . The determinant of a 2  2 matrix.

Warm UP: Review of Inequalities What do each of the symbols represent: 1. > 2. < Greater Than 2. Less than 3. Less than or equal to 4. Greater.

3.8B Solving Systems using Matrix Equations and Inverses.

Notes Over 4.3 Evaluate Determinants of 2 x 2 Matrices

Warm Up Multiple the matrices. 1. Find the determinant –1 0.

F UNDAMENTALS OF E NGINEERING A NALYSIS Eng. Hassan S. Migdadi Cramer’s Rule for solving linear systems Part 1.

Using Matrices to Solve a 3-Variable System

Use Inverse Matrices to Solve Linear Systems

Cramer’s Rule (because Cramer RULES!)

3-3: Cramer’s Rule.

Warm-up 1. Find A-1 , A = 2. Solve AX = B when B =

4.3 Determinants and Cramer’s Rule

Using Determinants to solve systems of equations

Applications of Matrices

Systems of Linear Equations

Section 6.4 Multiplicative Inverses of Matices and Matrix Equations

4.3 Determinants and Cramer’s Rule

Lesson 13-3: Determinants & Cramer’s Rule

Applying Determinants to solve Systems of Equations 2x2 & 3x3

Cramer’s Rule and Solving Systems of Equations

4-5 Matrix Inverses and Solving Systems Warm Up Lesson Presentation

Applications of Inverse Matrices

Evaluate Determinants & Apply Cramer’s Rule

Chapter 7: Matrices and Systems of Equations and Inequalities

Using matrices to solve Systems of Equations

Find the inverse of the matrix

Multiplicative Inverses of Matrices and Matrix Equations

Use Inverse Matrices to Solve 2 Variable Linear Systems

Students will write a summary explaining how to use Cramer’s rule.

Find the area of the Triangle

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:

4.3 Determinants and Cramer’s Rule

College Algebra Chapter 6 Matrices and Determinants and Applications

Using matrices to solve Systems of Equations

Solving Linear Systems of Equations - Inverse Matrix

Presentation transcript:

Notes Over 10.5 Using Cramer’s Rule for a 2 x 2 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix To find your x replace the x ’s in the coefficient Matrix with the constants To find your y replace the y ’s in the coefficient Matrix with the constants

Notes Over 10.5 Using Cramer’s Rule for a 3 x 3 System Use Cramer’s Rule to solve the linear system. Find the determinant of the coefficient Matrix

Find the area of the triangle with the given vertices. Notes Over 10.5 The Area of a Triangle Find the area of the triangle with the given vertices.

Determine whether the points lie on the same line. Notes Over 10.5 Test for Collinear Points Determine whether the points lie on the same line. Non-Collinear

Find an equation of the line through the two points. Notes Over 10.5 Equation of a Line Find an equation of the line through the two points.

Notes Over 10.5 Encoding a Message Use the code in the book and the matrix to encode the message. First, convert the letters to row matrices Then multiply each uncoded row by matrix A

Notes Over 10.5 C O O L M A N Decoding a Message Use the code in the book and the matrix to decode the message. C O O L M A N

Notes Over 10.5