Matrix Multiplication Sec. 4.2

Slides:

Advertisements

Similar presentations

Advertisements

2.3 Modeling Real World Data with Matrices

Section 13-4: Matrix Multiplication

Section 4.2 – Multiplying Matrices Day 2

Matrix Multiplication To Multiply matrix A by matrix B: Multiply corresponding entries and then add the resulting products (1)(-1)+ (2)(3) Multiply each.

Maths for Computer Graphics

Multiplying matrices An animated example. (3 x 3)x (3 x 2)= (3 x 2) These must be the same, otherwise multiplication cannot be done Is multiplication.

Matrices The Basics Vocabulary and basic concepts.

Table of Contents Matrices - Multiplication Assume that matrix A is of order m  n and matrix B is of order p  q. To determine whether or not A can be.

Determinants 2 x 2 and 3 x 3 Matrices. Matrices A matrix is an array of numbers that are arranged in rows and columns. A matrix is “square” if it has.

Row 1 Row 2 Row 3 Row m Column 1Column 2Column 3 Column 4.

4.2 Operations with Matrices Scalar multiplication.

Algebra 2: Lesson 5 Using Matrices to Organize Data and Solve Problems.

Different Types of Fields to Describe the Earth. Anisotropy, heterogeneity SEM of shale (Josh et al., 2012)

AIM: How do we perform basic matrix operations? DO NOW:  Describe the steps for solving a system of Inequalities  How do you know which region is shaded?

Multiplying Matrices Dr. Shildneck Fall, Can You Multiply Matrices? ›What do you think has to be true in order to multiply? ›What procedure do you.

If A and B are both m × n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding elements of A and B. add these.

3.6 – Multiply Matrices The product of two matrices A and B is defined provided the number of columns in A is equal to the number of rows in B. If A is.

4.1: Matrix Operations Objectives: Students will be able to: Add, subtract, and multiply a matrix by a scalar Solve Matrix Equations Use matrices to organize.

How to Multiply Two Matrices. Steps for Matrix Multiplication 1.Determine whether the matrices are compatible. 2.Determine the dimensions of the product.

8.2 Operations With Matrices

Matrix Operations.

2.2 Multiplying Matrices Mr. Anderson Pre Calculus Falconer Central High School Falconer, NY.

Sec 4.1 Matrices.

Multiplying Matrices Lesson 4.2. Definition of Multiplying Matrices The product of two matrices A and B is defined provided the number of columns in A.

Algebra Matrix Operations. Definition Matrix-A rectangular arrangement of numbers in rows and columns Dimensions- number of rows then columns Entries-

Warm Up Perform the indicated operations. If the matrix does not exist, write impossible

What is Matrix Multiplication? Matrix multiplication is the process of multiplying two matrices together to get another matrix. It differs from scalar.

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.

Matrix Multiplication The Introduction. Look at the matrix sizes.

Section 4.3 – Multiplying Matrices. MATRIX MULTIPLICATION 1. The order makes a difference…AB is different from BA. 2. The number of columns in first matrix.

3.6 Multiplying Matrices Homework 3-17odd and odd.

Chapter 1 Section 1.6 Algebraic Properties of Matrix Operations.

Notes Over 4.2 Finding the Product of Two Matrices Find the product. If it is not defined, state the reason. To multiply matrices, the number of columns.

Do Now: Perform the indicated operation. 1.). Algebra II Elements 11.1: Matrix Operations HW: HW: p.590 (16-36 even, 37, 44, 46)

Assignment Answers. 1.7: Multiplication with Matrices.

4-3 Matrix Multiplication Objective: To multiply a matrix by a scalar multiple.

§9-3 Matrix Operations. Matrix Notation The matrix has 2 rows and 3 columns.

Ch. 12 Vocabulary 1.) matrix 2.) element 3.) scalar 4.) scalar multiplication.

MATRIX MULTIPLICATION

Matrices. Matrix A matrix is an ordered rectangular array of numbers. The entry in the i th row and j th column is denoted by a ij. Ex. 4 Columns 3 Rows.

13.4 Product of Two Matrices

12-1 Organizing Data Using Matrices

Multiplying Matrices.

Sec. 4-3: Matrix Multiplication 8/24/17

Christmas Packets are due on Friday!!!

4-3 Multiplying Matrices

Matrix Multiplication

Multiplication of Matrices

Warm Up Use scalar multiplication to evaluate the following:

Multiplying Matrices.

WarmUp 2-3 on your calculator or on paper..

MULTIPLYING TWO MATRICES

Matrix Multiplication

MATRICES MATRIX OPERATIONS.

Objectives Multiply two matrices.

Warm-Up 3) 1) 4) Name the dimensions 2).

Multiplying Matrices.

Matrix Multiplication

Dimensions matching Rows times Columns

3.6 Multiply Matrices.

Matrix A matrix is a rectangular arrangement of numbers in rows and columns Each number in a matrix is called an Element. The dimensions of a matrix are.

Multiplying Matrices.

3.5 Perform Basic Matrix Operations Algebra II.

Multiplying Matrices.

Introduction to Matrices

Matrices - Operations MULTIPLICATION OF MATRICES

Multiplying Matrices.

Presentation transcript:

Matrix Multiplication Sec. 4.2

Matrix Multiplication #1 3 5 -2 1 4 9 5 2 3 4 X = 3 x 2 2 x 2 Must be equal

Matrix Multiplication #1 3 5 -2 1 4 9 5 2 3 4 __ X = 3 x 2 2 x 2 3 x 2 The resulting matrix size

Matrix Multiplication #2 5 3 -2 4 -1 X 2 1 3 4 5 6 = 3 x 2 2 x 4 Must be equal

Matrix Multiplication #2 5 3 -2 4 -1 __ X 2 1 3 4 5 6 = 3 x 2 2 x 4 3 x 4 The resulting matrix size

Matrix Multiplication #3 2 5 -2 1 4 6 9 Can not multiply these matrices X 2 1 3 4 5 6 2 x 4 3 x 3 not equal

Matrix Multiplication 3 5 -2 1 4 9 5 2 3 4 X Row by Column

Let’s Begin……….

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x 5 + 5 x 3 = 30

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x 5 + 5 x 3 = 30

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 = A(1,1)

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x 2 + 5 x 4 = 26

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x 2 + 5 x 4 = 26

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 = A(1,2)

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X -2 x 5 + 1 x 3 = -7

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X -2 x 5 + 1 x 3 = -7

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,1)

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x 2 + 1 x 4 = 0

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x 2 + 1 x 4 = 0

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,2)

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x 5 + 9 x 3 = 47

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x 5 + 9 x 3 = 47

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 = A(3,1)

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x 2 + 9 x 4 = 44

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x 2 + 9 x 4 = 44

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = A(3,2)

A Quick Review

Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 = A(1,1)

Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 = A(1,2)

Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,1)

Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,2)

Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 = A(3,1)

Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = A(3,2)

Matrix Multiplication 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 =

One Final Concept with Matrix Multiplication

Matrix Multiplication Not Commutative