module 6 matrices & applications chapter 26 matrices and applications i
TRANSCRIPT
Module 6Module 6
Matrices & Matrices &
ApplicationsApplications
Chapter 26Chapter 26
Matrices and Applications I
Matrices and Applications I
26.1
26.1
What
is a
Matr
ix?
What
is a
Matr
ix?
A matrix (plural matrices) is a rectangular array of numbers arranged in
rows and columns. The numbers in a
matrix are called the
elements of the matrix.
Matr
ix
Matr
ix
repre
senta
tion
repre
senta
tion
The ORDER of a matrix
= number of rows x number of columns
E.g. The matrix shown below has 3 rows and 2 columns.
We say that it is a 3 by 2 rectangular matrix and
its order is 3 by 2 (3 x
2).
Capital letters will be
used to represent matrices. In general, a matrix with
m rows and n columns is
known as an m x n
matrix. The elements in
a matrix are referred to
by the row and then by
the column position.
The element in the
second row and the first
column of matrix A is -1.
This is represented as
a21 = -1
Row
matr
ices
Row
matr
ices A matrix with one row
is called a row matrix
or row vector.
Colu
mn M
atr
ices
Colu
mn M
atr
ices A matrix with one
column is called a column matrix or column vector
Square
Matr
ices
Square
Matr
ices A matrix with an equal
number of rows and columns is called a square matrix
Matr
ix N
ota
tion
Matr
ix N
ota
tion
The location of each
The location of each element in the matrix
element in the matrix
is specified by its row
is specified by its row
and column number.
and column number.
Exa
mple
Exa
mple
A is a 1x 3 row matrix. The
number 3 is represented by
a13. B is a 3x3 diagonal matrix.
The element in the 2, 1
position is 0 and the number
3 is represented by b33.
C is a 3x 1 column matrix.
The element in the 2, 1
position is 1 and the number
3 is represented by c11.
D is a 2 . 4 matrix. The
element in the 2, 1 position
is 2 and the number 3 is
represented by d23.
E is not a matrix.
Ente
ring a
matr
ix
Ente
ring a
matr
ix
into
a g
raphic
s
into
a g
raphic
s ca
lcula
tor
calc
ula
tor
Refer to pages 695 &
Refer to pages 695 &
696 of your text book
696 of your text book
for notes on how to
for notes on how to enter a matrix on the
enter a matrix on the
Ti-Nspire CAS.
Ti-Nspire CAS.