, 8.1 Matrix Solutions to Linear Systems
Matrices
Matrices used to information and to solve systems of linear equations A The information
are
display .
matrix is a
rectangular array
.
is
arranged in rows and columns and placed in brackets .
The values inside the brackets are called elements of the matrix .
matrix > [ } }]
Notations for Matrices
An of numbers and columns and placed called matrix We represent two different
array , arranged in rows in brackets ,
is a .
can a matrix in
:
ways
•
A capital letter such as A. B or C can denote a matrix .
, , ,
•
A lowercase letter enclosed in brackets , such as [ aij ] can denote a matrix .
A A This refers ith and
general element in matrix is denoted by aij .
to the element in the row jth column .
A matrix of order mxn has m rows and n columns .
If matrix has the number of columns and called matrix
m=n ,
a same rows as is a
square .
2
a=[ 34 ]
1
2×2
Example
Let
a=f§ ¥ ] I 6
a. What is the order of A ? 3×2
b. -2
Identify
=
a ,z
I
Identify
=
C. a} ,
Augmented Matrices
An
The first step in
solving a
system of linear
equations using matrices is to write the augmented matrix .
augmented matrix has a
vertical bar
separating the columns of the matrix into two
groups .
The coefficients of each variable are placed to the left of the
vertical line and the constants are placed to the right If
any variable is its coefficient is 0
.
missing , .
Example
write the systems of matrix
equations as an
augmented .
{ I :]
3×+49-2=12 3 4 -
I 12
32=-15 > l l -3
✗ +
y
-
- -
0 9 2
9g -122=8
Matrices
Matrices used to information and to solve systems of linear equations A The information
are
display .
matrix is a
rectangular array
.
is
arranged in rows and columns and placed in brackets .
The values inside the brackets are called elements of the matrix .
matrix > [ } }]
Notations for Matrices
An of numbers and columns and placed called matrix We represent two different
array , arranged in rows in brackets ,
is a .
can a matrix in
:
ways
•
A capital letter such as A. B or C can denote a matrix .
, , ,
•
A lowercase letter enclosed in brackets , such as [ aij ] can denote a matrix .
A A This refers ith and
general element in matrix is denoted by aij .
to the element in the row jth column .
A matrix of order mxn has m rows and n columns .
If matrix has the number of columns and called matrix
m=n ,
a same rows as is a
square .
2
a=[ 34 ]
1
2×2
Example
Let
a=f§ ¥ ] I 6
a. What is the order of A ? 3×2
b. -2
Identify
=
a ,z
I
Identify
=
C. a} ,
Augmented Matrices
An
The first step in
solving a
system of linear
equations using matrices is to write the augmented matrix .
augmented matrix has a
vertical bar
separating the columns of the matrix into two
groups .
The coefficients of each variable are placed to the left of the
vertical line and the constants are placed to the right If
any variable is its coefficient is 0
.
missing , .
Example
write the systems of matrix
equations as an
augmented .
{ I :]
3×+49-2=12 3 4 -
I 12
32=-15 > l l -3
✗ +
y
-
- -
0 9 2
9g -122=8
