PDF chapter test

A matrix is represented in the form $$(\text{Number of rows})$$ $$\times$$ $$(\text{Number of column})$$.

Let us consider a matrix with the '$$m$$', the number of rows and '$$n$$', the number of columns.

Then the matrix is represented as $$m$$ $$\times$$ $$n$$.

$$m$$ $$\times$$ $$n$$ can be either be read as $$m$$ 'cross' $$n$$ or $$m$$ 'by' $$n$$.

The general form of a $$m$$ $$\times$$ $$n$$ matrix is given by:

Here, $$a_{11}$$, $$a_{12}$$, and so on are entries of a matrix.

The general form of an entry of a matrix is $$a_{ij}$$, where '$$i$$' represents the $$i^{th}$$ row of the matrix and '$$j$$' represents the $$j^{th}$$ column of the matrix. An entry of a matrix can also be represented as the $$(i$$, $$j)^{th}$$ element.

A matrix '$$A$$' can also be represented as $$A$$ $$=$$ $$(a_{ij})_{m \times n}$$ where $$i$$ $$=$$ $$1$$, $$2$$, $$3$$$$...m$$ and $$j$$ $$=$$ $$1$$, $$2$$, $$3...n$$.

The total number of elements in the matrix $$A$$ $$=$$ $$(a_{ij})_{m \times n}$$ is given by $$mn$$.

Important!
While representing the order of a matrix, we should always write the '$$\text{Number of rows}$$' first, followed by the '$$\text{Number of columns}$$'.
Example: