#### 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.