BUSINESS MATHEMATICS

&

STATISTICS

Lecture 8Discount_interest 1

LECTURE 9Review Lecture 8

Matrices

Matrix Applications using Excel

QestionsWhere can we use Matrices?

Typical applications? What is a Matrix?

What are Matrix operations?Excel Matrix Functions?

Where can we use Matrices?Many applications in business and industry

Where large amounts of data are processed daily

Typical ApplicationsPractical questions in modern business and economic

management using econometrics

Network Analysis

Decision Networks

Optimization

(Linear Programming)

Analysis of data

Computer graphics

What is a Matrix?A Matrix is a rectangular array of numbers

The plural of matrix is matrices

Matrices are usually represented with capital letters

Matrices A, B, C

  Size

Youth S M L XL

Pants 0 10 34 40 12

Shirts 18 25 29 21 7

Shorts 19 13 48 36 9

T-shirts 27 7 10 24 14

DimensionDimension or Order of a Matrix =

Number of Rows x Number of Columns

ExampleMatrix T has dimensions of 2x3

or the order of matrix T is 2x3

    

Row, column and Square MatrixRow Matrix dimensions 1xn

Column Matrix matrix with dimensions nx1

Square Matrix matrix with dimensions nxn

Row Matrix Example: Matrix A = 1x4

Column Matrix Example: Matrix B = a 2x1

Square Matrix Example: Matrix C = a 3x3

Identity MatrixA square matrix with 1's on the main

diagonal from the upper left to the lower right and 0's off the main

diagonal.

Denoted as I

Subscript indicates the size of the identity matrix

represents an identity matrix with dimensions nxn. 

Multiplicative IdentityWith real numbers, the number 1 is referred to as a multiplicative identity Unique property: product a real

number and 1 is that real number.1 is called a multiplicative identity

For any real number n,

1x n = n and n x1 = n.

Multiplicative IdentityWith matrices, the identity matrix shares the same unique

property as the number 1.

A 2x2 identity matrix is a multiplicative inverse because for any 2x2 matrix A, I2xA = A and AxI2 = A

BUSINESS MATHEMATICS

&

STATISTICS

Example 1An athletic clothing company manufactures T-shirts and

sweat shirts in four differents sizes, small, medium, large, and x-large. The company supplies two major

universities, the U of R and the U of S. The tables below show September's clothing order for each university

University of S's September Clothing Order S M L XL T-shirts 100 300 500 300Sweat shirts 150 400 450 250 

University of R's September Clothing Order S M L XL

T-shirts 60 250 400 250Sweat shirts 100 200 350 200

Matrix Representation

The above information can be given by two matrices S and R as shown to the right

Matrix OperationsOrganize and interpret data using matrices

Use matrices in business applicationsAdd and subtract two matrices

Multiply a matrix by a scalarMultiply two matrices

Interpret the meaning of the elements within a product matrix

+

=

ADDITION

PRODUCTION

The clothing company production in preparation for the universities'

Septmber orders is shown by the table and corresponding matrix, P=

Over-Production

-

=

+

=

ADDITION

Addition and Subtraction of Matrices

The sum or difference of two matrices is caluculated by adding or subtracting the

corresponding elements of the matrices

To add or subtract matrices, they must have the same

dimensions.

POSSIBLE ?

YES

YES

No

MULTIPLICATION

591mL 1L 2L

Company A 20,000 5,500 10,600

Company B 18,250 7,000 11,000

Price 1.60 2.30 3.10

What is total revenue of Company A?

What is total revenue of Company B?

MULTIPLICATION

S= P= R=

20,000x1.6+5,500x2.3+10,600x3.1= 77,510

18,250x1.6+7,000x2.3+11,000x3.1=79,400

Matrix Functions in Microsoft Excel

MDETERM   Returns the matrix determinant of an array

MINVERSE 

  Returns the matrix inverse of an array

MMULT   Returns the matrix product of two arrays

MULTIPLICATION

591mL 1L 2L

Company A 20,000 5,500 10,600

Company B 18,250 7,000 11,000

Price 1.60 2.30 3.10

What is total revenue of Company A?

What is total revenue of Company B?

MULTIPLICATION

S= P= R=

20,000x1.6+5,500x2.3+10,600x3.1= 77,510

18,250x1.6+7,000x2.3+11,000x3.1=79,400