JEE Main & Advanced Mathematics Determinants & Matrices Order of a Matrix

Order of a Matrix

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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