If A is a matrix of order m × n, then,
A =
⎟⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎜
⎝
⎛
m 1 m 2 m 3 mn
31 32 33 3 n
21 22 23 2 n
11 12 13 1 n
a
...
...
...
a
...
a
...
a
...
a a a ... a
a a a ... a
a a a ... a
m^ ×^ n
Note : LEADING DIAGONAL
A = ⎟⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
31 32 33
21 22 23
11 12 13
a a a
a a a
a a a
In the above matrix the elements of the leading diagonal are a 11 , a 22 , a 33.
- Order of a Matrix
The order of a matrix is given by the number of rows into the number of columns of
the matrix. For example, if a matrix has 3 rows and 4 columns then the order of the
matrix is denoted as 3×4. Note that the sign ‘×’ between the rows and columns does
not denote multiplication. Also note that a matrix with 3 rows and 4 columns will
contain 3×4=12 elements. In general, if a matrix has ‘m’ rows and ‘n’ columns then
the matrix will consist of ‘mn’ elements. The elements of a matrix are also called as
entries of the matrix.
Eg. : A = ⎟⎟
⎠
⎞
⎜⎜⎝
⎛
− −
− −
2 3 4
1 2 3
Here the matrix A has 2 rows and 3 columns and hence the order of the matrix is
2 × 3. Also note that the total number of elements in the matrix is 2×3 = 6.
Once the child is clear with the concept of matrix, the method of finding the number
of elements in a matrix can be taught with the help of magnetic board where rows and
columns are arranged.
