8.4 Matrix Operations Day 1 Thurs May 7 Do Now Solve X – 2y = -6 3x + 4y = 7.

Slides:

Advertisements

Similar presentations

Advertisements

2.3 Modeling Real World Data with Matrices

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

Objective Video Example by Mrs. G Give It a Try Lesson 4.1  Add and subtract matrices  Multiply a matrix by a scalar number  Solve a matrix equation.

4.1 Using Matrices to Represent Data

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.

Chapter 4 Matrices By: Matt Raimondi.

4.1 Matrix Operations What you should learn: Goal1 Goal2 Add and subtract matrices, multiply a matrix by a scalar, and solve the matrix equations. Use.

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

1 C ollege A lgebra Systems and Matrices (Chapter5) 1.

Unit 3: Matrices.

13.1 Matrices and Their Sums

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.

Class Opener:. Identifying Matrices Student Check:

Prepared by Deluar Jahan Moloy Lecturer Northern University Bangladesh

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.

Chapter 6 Systems of Linear Equations and Matrices Sections 6.3 – 6.5.

Notes 7.2 – Matrices I. Matrices A.) Def. – A rectangular array of numbers. An m x n matrix is a matrix consisting of m rows and n columns. The element.

4.1 Using Matrices Warm-up (IN) Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar.

Matrix Algebra Section 7.2. Review of order of matrices 2 rows, 3 columns Order is determined by: (# of rows) x (# of columns)

8.2 Operations With Matrices

Matrices: Simplifying Algebraic Expressions Combining Like Terms & Distributive Property.

Matrix Operations.

MATRICES MATRIX OPERATIONS. About Matrices  A matrix is a rectangular arrangement of numbers in rows and columns. Rows run horizontally and columns run.

MATRICES Danny Nguyen Marissa Lally Clauberte Louis HOW TO'S: ADD, SUBTRACT, AND MULTIPLY MATRICES.

Sec 4.1 Matrices.

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

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.

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.

3.5 Perform Basic Matrix Operations Add Matrices Subtract Matrices Solve Matric equations for x and y.

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

Systems of Equations and Matrices Review of Matrix Properties Mitchell.

Where do you sit?. What is a matrix? How do you classify matrices? How do you identify elements of a matrix?

Matrix – is a rectangular arrangement of numbers in rows and columns. Dimensions – Size – m is rows, n is columns. m x n ( row ∙ column) Elements – The.

12-2 MATRIX MULTIPLICATION MULTIPLY MATRICES BY USING SCALAR AND MATRIX MULTIPLICATION.

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.

MATRICES. Introduction Matrix algebra has several uses in economics as well as other fields of study. One important application of Matrices is that it.

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

Chapter Seven Linear Systems and Matrices. Warm-up #1 The University of Georgia and Florida State University scored a total of 39 points during the 2003.

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.

Sections 2.4 and 2.5 Matrix Operations

12-1 Organizing Data Using Matrices

Multiplying Matrices.

Christmas Packets are due on Friday!!!

Warm-Up - 8/30/2010 Simplify. 1.) 2.) 3.) 4.) 5.)

Matrix Multiplication

Matrix Operations Monday, August 06, 2018.

Matrix Operations.

Basic Matrix Operations

Matrix Operations SpringSemester 2017.

Section 7.4 Matrix Algebra.

Matrix Algebra.

MATRICES MATRIX OPERATIONS.

4.1 Matrices – Basic Operations

MATRICES MATRIX OPERATIONS.

Matrices and Matrix Operations

Section 11.4 Matrix Algebra

Matrix Algebra.

3.6 Multiply Matrices.

Matrix Operations Ms. Olifer.

What is the dimension of the matrix below?

Matrix Operations SpringSemester 2017.

3.5 Perform Basic Matrix Operations Algebra II.

Presentation transcript:

8.4 Matrix Operations Day 1 Thurs May 7 Do Now Solve X – 2y = -6 3x + 4y = 7

Matrices A matrix is an organization of numbers in a rectangular form

Matrices The rows of a matrix are horizontal The columns are vertical A matrix with m rows and n columns is said to be of order m x n The numbers in a matrix are called entries The main diagonal starts from the top left and travels down and to the right

Matrix Operations Matrix Addition and Subtraction Scalar Multiplication Matrix Multiplication

Matrix Addition and Subtraction Given Matrix A and B with the same order A + B = add corresponding entries A – B = subtract corresponding entries

Ex Find A + B for

Ex Find C – D for

You try Find A + B for

Additive Inverse The additive inverse of a matrix is obtained by replacing each entry with its opposite

Ex Find –A and A + (-A) given

Scalar Multiplication The scalar product of a number k and a matrix A is the matrix kA, obtained by multiplying each entry of A by the number k

Ex Find 3A and (-1)A for

Ex P.716

Matrix Multiplication When multiplying 2 matrices, there is a prerequisite that must be satisfied, or it cannot happen Matrix: Dimensions: The two inside dimensions must be equal, or the multiplication is not defined Note: Just because AB exists, doesn’t mean that BA also exists

Can we multiply these matrices? 1) 2) 3)

Multiplying Matrices To multiply, take the 1st row of matrix A and the 1st column of Matrix B – Multiply each corresponding element, and then add them together to get each new element

Ex Let Find 1) AB 2) BA 3) BC 4) AC

Closure Multiply AB given HW: p.720 #1-27 odds

8.4 Matrix Operations Day 2 Fri May 8 Do Now Find AB given

HW Review: p.720 #1-27

Properties of Matrix Multiplication A(BC) = (AB)C A(B + C) = AB + AC (B + C)A = BA + CA Note that property 2 and 3 result in different matrices

Word problems When constructing a matrix from a word problem, the rows and columns should represent different types of the same thing (rows: types of cookies) (columns: amount of sugar)

Ex7 P.718

Matrix Equations We can write a system of equations into a matrix equation by making each column equivalent to a variable

Ex Write the following system into a matrix equation 4x + 2y – z = 3 9x + z = 5 4x + 5y – 2z = 1

Closure What must be true when multiplying matrices? Adding matrices? HW: p.720 #29-45 odds