Post on 20-Jan-2016
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