PPT - Matrices and Determinants | Business Mathematics and Statistics - B Com PDF Download

 Page 1


1
Matrices and Determinants
Page 2


1
Matrices and Determinants
1. Matrices
2. Operations of matrices
3. Types of matrices
4. Properties of matrices
5. Determinants
6. Inverse of a 3 ?3 matrix
2
Page 3


1
Matrices and Determinants
1. Matrices
2. Operations of matrices
3. Types of matrices
4. Properties of matrices
5. Determinants
6. Inverse of a 3 ?3 matrix
2
?
2 3 7
?
3
A ?
?
?
?
1 ? 1 5
?
1.1 Matrices
4
?
?
1 3 1
?
B ?
?
2 1 
7
? ?
?
?
4 6
?
?
Both A and B are examples of matrix. A matrix 
is a rectangular array of numbers enclosed by a 
pair of bracket.
Why matrix?
Page 4


1
Matrices and Determinants
1. Matrices
2. Operations of matrices
3. Types of matrices
4. Properties of matrices
5. Determinants
6. Inverse of a 3 ?3 matrix
2
?
2 3 7
?
3
A ?
?
?
?
1 ? 1 5
?
1.1 Matrices
4
?
?
1 3 1
?
B ?
?
2 1 
7
? ?
?
?
4 6
?
?
Both A and B are examples of matrix. A matrix 
is a rectangular array of numbers enclosed by a 
pair of bracket.
Why matrix?
How about solving
4
?
?
x ?y ?7,
?
3x ?y ?5.
?
?
?
?
?
?
x ? y ? 2z ? 7,
2x ? y ? 4z ? 2,
?
?5x ? 4y ?10z ? 1,
3x ? y ? 6z ? 5.
Consider the following set of equations:
It is easy to show that x = 3 and
y = 4.
Matrices can help …
1.1 Matrices
Page 5


1
Matrices and Determinants
1. Matrices
2. Operations of matrices
3. Types of matrices
4. Properties of matrices
5. Determinants
6. Inverse of a 3 ?3 matrix
2
?
2 3 7
?
3
A ?
?
?
?
1 ? 1 5
?
1.1 Matrices
4
?
?
1 3 1
?
B ?
?
2 1 
7
? ?
?
?
4 6
?
?
Both A and B are examples of matrix. A matrix 
is a rectangular array of numbers enclosed by a 
pair of bracket.
Why matrix?
How about solving
4
?
?
x ?y ?7,
?
3x ?y ?5.
?
?
?
?
?
?
x ? y ? 2z ? 7,
2x ? y ? 4z ? 2,
?
?5x ? 4y ?10z ? 1,
3x ? y ? 6z ? 5.
Consider the following set of equations:
It is easy to show that x = 3 and
y = 4.
Matrices can help …
1.1 Matrices
21
?
?
?
? m1 m2 mn ?
5
a
1n
?
2n
?
?
?
a
11
a
12
?
a
22
a a
A ?
?
?
a
a a
In the matrix
?numbers a
ij
are called elements. First subscript 
indicates the row; second subscript indicates 
the column. The matrix consists of mn elements
?It is called “the m ? n matrix A = [a
ij
] ” or simply 
“the matrix A ” if number of rows and columns 
are understood.
1.1 Matrices