Identity and Inverse Matrices. Key Topics Identity matrix: a square matrix, multiplied with another matrix doesn’t change the other matrix (just like.

Slides:

Advertisements

Similar presentations

PRECALCULUS 2 Determinants, Inverse Matrices & Solving.

Advertisements

4.5 2x2 Matrices, Determinants and Inverses

Identity and Inverse Matrices

Properties The additive inverse property tells us to simply take a number and add its opposite so we get zero. Example 1 -6 is the additive inverse of.

4.5 Inverses of Matrices.

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.

Warm-up 23-1 A = 0-54 B = C = 9 4 D = Find 8A 2. Find AC 3. Find CD 4. Find BD.

1.8 Properties of Real Numbers. Commutative (Addition) The “you can switch it around and it just don’t matter” property a + b = b + a.

Finding the Inverse of a Matrix

Using Matrices to Solve a 3-Variable System

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,

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.

4-6 3x3 Matrices, Determinants, & Inverses

4.5, x 2 and 3 x 3 Matrices, Determinants, and Inverses Date: _____________.

Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.

Commutative Property of Addition 2+3 = 3+2 *This property states you can add two numbers in any order!

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

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.

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

Objectives Determine whether a matrix has an inverse.

Today: Class Announcements Class Announcements Wednesday Warm-Up Wednesday Warm-Up 4.4 Notes 4.4 Notes Begin Homework Begin Homework Return Quizzes.

Chapter 2 Systems of Linear Equations and Matrices

Inverse & Identity Matrices

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

Ch X 2 Matrices, Determinants, and Inverses.

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.

 1 is the multiplicative identify for real #’s : 1· a=a and a· 1 = a  For matrices n X n, the identity matrix has 1’s on its main diagonals and 0’s.

Warm Up. Inverse Matrices Three main topics today Identity Matrix Determinant Inverse Matrix.

Chapter 4 Section 4: Inverse and Identity Matrices 1.

Warm-Up 3) Find the determinant by hand. 4) Find the determinant using your calculator. 1) Multiply. Show work. 2) Multiply. Show work.

Identity & Inverse Matrices

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

The Matrix Reloaded

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.

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

2x2 Matrices, Determinants and Inverses

Find the determinate of both of the following matrices.

4-5 – 2x2 Matrices, Determinants, & Inverses. Objectives Evaluating Determinants of 2x2 Matrices Using Inverse Matrices to Solve Equations.

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

2.5 – Determinants and Multiplicative Inverses of Matrices.

Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve.

1-4 Properties of Real Numbers. Properties 1.Additive Identity – the sum of any number and zero is equal to the number. a + 0 = a 2.Multiplicative Identity.

Inverse Properties.

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.

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

Using Matrices to Solve a 3-Variable System

4-2 Multiplying Matrices Warm Up Lesson Presentation Lesson Quiz

Ch. 7 – Matrices and Systems of Equations

Finding the Inverse of a Matrix

Matrix Operations Add and Subtract Matrices Multiply Matrices

Solving Matrix equations

Use Inverse Matrices to Solve Linear Systems

Solving Linear Systems Using Inverse Matrices

27. Determinants and Inverses

Unit 3: Matrices

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

Commutative Property Associative Property A. Addition

3.8 Use Inverse Matrices to Solve Linear Systems

5 minutes Warm-Up Multiply Matrix A times Matrix B.

Bellwork 1) Multiply. 3) Find the determinant. 2) Multiply.

Lesson 4: Inverses of Matrices (part 1)

Commutative Property Associative Property A. Addition

The Identity and Inverse Matrices

Check even answers p.76: Hint: One of the problems on p.76 has

Presentation transcript:

Identity and Inverse Matrices

Key Topics Identity matrix: a square matrix, multiplied with another matrix doesn’t change the other matrix (just like 1 is the multiplicative identity of real numbers)

Identity Matrix in Action Notice: These two matrices are the same. Multiplying by the identity matrix changed nothing

Key Topics You might be wondering: why do I tell you about the identity matrix ?? If it doesn’t do anything, why do we need to know what it is ?? Inverses: two nXn matrices are inverses of each other if their product is the identity matrix

Checking for Inverse Matrices Determine whether the following pairs of matrices are inverses of one another:

Finding 2X2 Inverse Matrices To find the inverse of a 2X2 matrix, use the following method: Basically this tells us to calculate the determinant, then multiply it’s inverse by the rearranged matrix having a and d switch places and b and c as the opposite values Inverse of Determinant Rearranged matrix A -1 is the notation used to represent the inverse of matrix A If determinant is 0 there is no inverse!!

Practice Find the inverse matrix for the following matrices: N/A