Chapter#3-Matrices & Determinants 1st Year-Mathematics-Punjab Board-Federal Board

2. MATRICES &
DETERMINANTS

3. Background:

4. MATRICES:

5. Types Of Matrices:

6.  Row Matrix:
A matrix having single row is called Row Matrix.
e.g.
B=[1 4 6]

7.  Column Matrix:
A matrix having single column is called
column Matrix.
e.g.
1
A= 4
7

8.  Square Matrix:
A matrix in which no of rows and columns are
equal is called square matrix.
e.g.
2 3
B=
1 7

9.  Rectangular Matrix:
A matrix in which no of rows and columns are
not equal is called square matrix.
e.g.
D= 1 4 6
7 3 1

10.  Diagonal Matrix:
A square matrix having each of its elements
excepts principle diagonal equal to zero and
at least one elements in its principle diagonal
matrix.
e.g.
1 0 0
S= 0 2 0
0 0 3

11.  Zero Matrix:
A square or rectangular matrix whose each element is zero, is called a null
or zero matrix.
It is denoted by O(m×n).
e.g.
O2×2=
0 0
0 0

12.  Scalar Matrix:
A square matrix having same elements in
principle diagonal except 1 is called scalar
matrix.
e.g.
k 0 0
A= 0 k 0
0 0 k

13.  Unit or Identity Matrix:
The identity matrix of size n is
the n × n square matrix with ones on
the main diagonal and zeros elsewhere. It is
denoted by In or simply by I.
1 0 0
I= 0 1 0
0 0 1

14.  Equal Matrix:
Two matrix are said to be equal if they are of
same order with the same correspondence
elements.
e.g.
3 5 3 5
A= B=
3 0 3 0

15.  Triangular Matrix:
UpperTriangular Matrix:
If all elements below the principle diagonal of
square matrix are zero then it is called upper
triangular matrix.
1 4 6
B= 0 1 3
0 0 1

16.  Triangular Matrix:
LowerTriangular Matrix:
If all elements above the principle diagonal of
square matrix are zero then it is called lower
triangular matrix.
1 0 0
B= 0 1 0
2 4 6

17. Operation of Matrices:

18. Problem for Practice: