Category : JEE Main & Advanced
A matrix having \[m\] rows and \[n\] columns is called a matrix of order \[m\times n\] or simply \[m\times n\] matrix (read as an \[m\] by \[n\] matrix). A matrix A of order \[m\times n\] is usually written in the following manner
\[A=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} & {{a}_{13}} & ...{{a}_{1j}} & ...{{a}_{1n}} \\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}} & ...{{a}_{2j}} & ...{{a}_{2n}} \\ ..... & ..... & ..... & ..... & ..... \\ {{a}_{i1}} & {{a}_{i2}} & {{a}_{i3}} & ...{{a}_{ij}} & ...{{a}_{in}} \\ ..... & ..... & ..... & ..... & ..... \\ {{a}_{m1}} & {{a}_{m2}} & {{a}_{m3}} & ...{{a}_{mj}} & ...{{a}_{mn}} \\ \end{matrix} \right]\,\text{or }A={{[{{a}_{ij}}]}_{m\times n}}\],
where \[\begin{align} & i=1,\,\,2,.....m \\ & j=1,\,\,2,.....n \\ \end{align}\]
Here \[{{a}_{ij}}\]denotes the element of \[{{i}^{th}}\] row and \[{{j}^{th}}\] column.
Example : order of matrix \[\left[ \begin{matrix} 3 & -1 & 5 \\ 6 & 2 & -7 \\ \end{matrix} \right]\]is \[2\times 3\]
A matrix of order \[m\times n\] contains \[mn\] elements. Every row of such a matrix contains \[n\] elements and every column contains \[m\] elements.
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