Matrix order and information

A matrix is a rectangular array. Its order is rows \(\times\) columns. An entry is located by its row first, then its column. A row matrix has one row, a column matrix one column, and a square matrix equal numbers of rows and columns.

Example

Two shops sell pens and notebooks. Rows represent East, West; columns represent pens, notebooks. The quantities sold are \(S=\begin{pmatrix}12&5\\8&9\end{pmatrix}\).

\(S\) has order \(2\times2\). The entry in row \(2\), column \(1\) is \(8\): West sold eight pens. Stating the row and column meanings makes the numbers interpretable.

Equal matrices have the same order and equal corresponding entries. If \(\begin{pmatrix}x&4\\2&y\end{pmatrix}=\begin{pmatrix}7&4\\2&-3\end{pmatrix}\), then \(x=7\), \(y=-3\). A zero matrix has every entry zero; its order still matters.