# Order of a Matrix

#### notes

A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix (read as an m by n matrix). So referring to the above examples of matrices, we have A as 3 × 2 matrix, B as 3 × 3 matrix and C as 2 × 3 matrix. We observe that A has 3 × 2 = 6 elements, B and C have 9 and 6 elements, respectively.
In general, an m × n matrix has the following rectangular array:

$\begin{bmatrix} a_{11} & a_{12} & a_{13} \cdots & a_{1j} \cdots & a_{1n} \\ a_{21} & a_{22} & a_{23} \cdots & a_{2j} \cdots & a_{2n}\\ \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{i1} & a_{i2} & a_{i3} \cdots & a_{ij} \cdots & a_{in} \\ \vdots & \vdots & \vdots & \vdots & \vdots \\a_{m1} & a_{m2} & a_{m3} \cdots & a_{mj} \cdots & a_{mn}\end{bmatrix}_{m × n}$

or A = [a_(ij)] _(m xx  n) , 1 <= i <= m , 1<= j <=n i , j  ∈  N
Thus the i^th  row consists of the elements a_(i1), a_(i2), a_(i3),..., a_("in"), while the jth column consists of the elements a_(1j), a_(2j), a_(3j),..., a_(mj),
In general a_(ij), is an element lying in the i^(th) row and j^(th) column. We can also call it as the (i, j)^(th) element of A. The number of elements in an m × n matrix will be equal to mn.

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