4.7 Identity and Inverse Matrices. What is an identity? In math the identity is the number you multiply by to have equivalent numbers. For multiplication.

Slides:

Advertisements

Similar presentations

Determinant The numerical value of a square array of numbers that can be used to solve systems of equations with matrices. Second-Order Determinant (of.

Advertisements

Identity and Inverse Matrices

Fractions. ADDING FRACTIONS  Build each fraction so that the denominators are the same  ADD the numerators  Place the sum of the two numerators on.

Inverses of n x n Matrices. The Inverse Matrix If A is an n x n matrix, the inverse of A (call it A -1 ) is the matrix such that A * A -1 is equal to.

Table of Contents Matrices - Inverse of a 2  2 Matrix To find the inverse of a 2  2 matrix, use the following pattern. Let matrix A be given by... Then.

4.3 The Inverse of a Matrix Warm-up (IN)

Table of Contents Matrices - Inverse Matrix Definition The inverse of matrix A is a matrix A -1 such that... and Note that... 1) For A to have an inverse,

 Definition: An Identity Matrix is a square matrix that, when multiplied by another matrix, equals the same matrix.  Form: In the Identity Matrix the.

Investigation 2.2 Missing Factors

Multiplying and Dividing Real Numbers. Language Goal  Students should be able to explain how to perform multiplication and division with real numbers.

F UNDAMENTALS OF E NGINEERING A NALYSIS Eng. Hassan S. Migdadi Inverse of Matrix. Gauss-Jordan Elimination Part 1.

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

Determinants and Multiplicative Inverses of Matrices

Converting Fractions to Decimals

Matrix Determinants and Inverses

Inverse & Identity Matrices

Lesson 7.6 & 7.7 Inverses of a Square Matrix & Determinant.

Ch X 2 Matrices, Determinants, and Inverses.

What you will learn 1. What an identity matrix is

4.7 Identity and Inverse Matrices and Solving Systems of Equations Objectives: 1.Determine whether two matrices are inverses. 2.Find the inverse of a 2x2.

Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.

Unit 3: Matrices.

Chapter 4 Section 4: Inverse and Identity Matrices 1.

Identity & Inverse Matrices

Inverse and Identity Matrices Can only be used for square matrices. (2x2, 3x3, etc.)

Dividing Fractions and Mixed Numbers Objective: Learn to divide fractions and mixed numbers.

Fraction Review TAKE NOTES!!!!!!. Vocabulary Numerator: the number on top in a fraction Denominator: the number on bottom in a fraction Example: What.

Properties of Multiplication The properties for multiplying whole numbers are also true for multiplying fractions and whole numbers. (only 1 new property)

Operations with Fractions. Adding and Subtracting Fractions.

Properties of Operations in Math Lesson 2. Inverse Operations Means: “putting together” a problem and “taking it apart” using the same numbers by + and.

INVERSE MATRICES Will Lombard, Meg Kelly, Sarah Bazir.

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

EQUIVALENT FRACTIONS. Math Vocabulary Equivalent fraction(s): Fractions that are EQUAL to each other, even though they look different.

4.5 Matrices, Determinants, Inverseres -Identity matrices -Inverse matrix (intro) -An application -Finding inverse matrices (by hand) -Finding inverse.

Today’s Plan: -Compare and order decimals -Human Number Line -Compare and order fractions 11/17/10 Compare and Order Rational Numbers Learning Target:

2.5 Determinants and Multiplicative Inverses of Matrices. Objectives: 1.Evaluate determinants. 2.Find the inverses of matrices. 3.Solve systems of equations.

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.

2.5 – Determinants and Multiplicative Inverses of Matrices.

Chapter 1 Section 1.6 Algebraic Properties of Matrix Operations.

9.1 Simplifying Rational Expressions Objectives 1. simplify rational expressions. 2. simplify complex fractions.

Unit 3: Matrices. Matrix: A rectangular arrangement of data into rows and columns, identified by capital letters. Matrix Dimensions: Number of rows, m,

+ Fractions. + Part of a whole + + Numerator How many pieces The number on the top of a fraction.

7 th Grade Math Vocabulary Word, Definition, Model Emery Unit 1.

13.3 Product of a Scalar and a Matrix.  In matrix algebra, a real number is often called a.  To multiply a matrix by a scalar, you multiply each entry.

Sections 2-1, 2-2, 2-3. Notes Identity Property of Addition: x + 0 = x ex: = 5 The opposite of a number is its additive inverse: x + -x = 0 ex:

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

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

College Algebra Chapter 6 Matrices and Determinants and Applications

Use Inverse Matrices to Solve Linear Systems

12-4: Matrix Methods for Square Systems

2-2 Solving One-Step Equations

The Inverse of a Square Matrix

10.5 Inverses of Matrices and Matrix Equations

Simplifying Square roots

B: Fractions, Decimals, and Percents

Equivalent Fractions.

Determinants and Multiplicative Inverses of Matrices

Equivalent Fractions: Ordering Fractions by Making Common Denominators

Use Inverse Matrices to Solve Linear Systems

Multiplying Matrices.

Solving Linear Systems Using Inverse Matrices

Equivalent Fractions: Creating Common Denominators

Unit 3: Matrices

Inverse & Identity MATRICES Last Updated: October 12, 2005.

2-2 Solving One-Step Equations

“ I can create equivalent forms of fractions, decimals, and percents.”

Lesson 4: Inverses of Matrices (part 1)

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

Presentation transcript:

4.7 Identity and Inverse Matrices

What is an identity? In math the identity is the number you multiply by to have equivalent numbers. For multiplication it is one. 5 * 1 = 5, of course. How is this useful? If you need to have a denominator of 40 in the fraction

What is an inverse? The inverse is a number when multiplied by another number equals one.

The identity matrix is a square matrix with one down the diagonals In a 2 X 2In a 3 X 3

Find the matrices that when multiply together are the identity matrix. How do we find the inverse?

Find the inverse Find the determinant of 6 – ( - 8) = 14 We will flip the diagonal of top left and bottom right, then change the signs the bottom left to top right diagonal.

Putting the part together Take the determinant and put it under one and multiply it by the moved matrix.

Lets see if it works

Can there be matrices without inverses? Yes, when the determinate equals zero. Since a fraction can not have zero for a denominator. There would be no inverse.

Homework Page 199 #