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TIF 21101
APPLIED MATH 1
(MATEMATIKA TERAPAN 1)
Week 6
Matrices
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Overview
You have already known that matrices used
throughout the discrete mathematics can express the
relationships between elements (data/entries) in sets.
Frequently, the data is arranged in arrays, that is, sets
whose elements are indexed by one or more subscripts.
Technically speaking, matrices will be used in
models of communications networks and transportation
systems. And there are many algorithms will be developed
that use these matrix models.
We shall begin our discussion into two parts, those
are less and more than 3-order matrices.
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Objectives
Definition of matrix and its components
The Arithmatic operation of matrix
Transpose of matrix
Determinant
Matrix Inversion
Multiplying operation between matrix
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Definition of matrix and its components
A matrix is a rectangular array of data/entries
A matrix with m rows and n columns is called an m x n matrix (read:
m by n matrix). A matrix with the same number of rows as columns is
called square matrix.
Two matrices are equal if they have the same number of rows and the
same number of columns and the corresponding entries in every
position are equal.
A one-dimensional array of data/entries is called a vector.
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Index
Columns (n)
Rows (m)
Entry
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Set A = {1,2,3,4,5,6,7}
In matrix becomes
[A] = [ 1 2 3 4 5 6 7 ] Vector A
In matrix becomes
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Or in linear equation :
2x + 2y = 16 ……………….(a)
x + 3y = 18 ………………...(b)
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The Arithmatic operation of matrix
Addition and Subtraction
Multiplying with scalar
Addition or Substraction of two or more
matrices needs the same index of them.
± ±
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Multiplying scalar with a matrix basically
multiplying a scalar with all entries of matrix
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Transpose of Matrix
Basically, it just changes rows into columns
Let A = [aij] be an m x n matrix. The transpose of
A, denoted by AT, is the n x m matrix obtained by
interchanging the rows and columns of A, AT=[aji].
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Determinant
To each n-square matrix A = [aij], we assign
a specific number called the determinant of
A and denoted by det [A] or |A|
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The determinants of order 1, 2, and 3 are
defined as follows:
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The following diagram may help you to find
the determinant of order 2:
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The following diagram may help you to find
the determinant of order 3:
How about the order of 4, 5, 6,…?
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Examples:
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Exercises :
Find
(a) A+B;
(b) (b) 3A and -4B
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Find the transposition of :
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