# Intro to matrices

Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements.
A matrix is a rectangular arrangement of numbers into rows and columns.
For example, matrix $A$ has two rows and three columns.

## Matrix dimensions

The dimensions of a matrix tells its size: the number of rows and columns of the matrix, in that order.
Since matrix $A$ has $\blueD{\text{two rows}}$ and $\goldD{\text{three columns}}$, we write its dimensions as $\blueD2 \times \goldD3$, pronounced "two by three".
In contrast, matrix $B$ has $\blueD{\text{three rows}}$ and $\goldD{\text{two columns}}$, so it is a $\blueD3\times \goldD2$ matrix.
$B=\left[\begin{array}{rr}-8 & -4 \\ 23 & 12 \\18 &10 \end{array}\right]$
When working with matrix dimensions, remember $\blueD{\text{rows}} \times \goldD{\text{columns}}$!

For example, consider matrix $G$:
$G=\left[\begin{array}{rr}4& 14&-7 \\ 18 & 5&13 \\-20 &4&22 \end{array}\right]$
The element $g_{\blueD2,\goldD1}$ is the entry in the $\blueD{\text{second row}}$ and the $\goldD{\text{first column}}$.
In this case $g_{2,1}=\maroonD{18}$.
In general, the element in $\blueD{\text{row } i}$ and $\goldD{\text{column }j}$ of matrix $A$ is denoted as $a_{\blueD i,\goldD j}$.