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## Precalculus

### Course: Precalculus>Unit 7

Lesson 1: Introduction to matrices

# 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 $\text{two rows}$ and $\text{three columns}$, we write its dimensions as $2×3$, pronounced "two by three".
In contrast, matrix $B$ has $\text{three rows}$ and $\text{two columns}$, so it is a $3×2$ matrix.
$B=\left[\begin{array}{rr}-8& -4\\ 23& 12\\ 18& 10\end{array}\right]$
When working with matrix dimensions, remember $\text{rows}×\text{columns}$!

1) What are the dimensions of matrix $D$?
$×$

2) What are the dimensions of matrix $E$?
$E=\left[\begin{array}{rrrr}-2& 6& 1& 3\\ 0& -8& 3& 10\end{array}\right]$
$×$

3) What are the dimensions of matrix $F$?
$F=\left[\begin{array}{r}-2\\ 0& \\ 10\end{array}\right]$
$×$

## Matrix elements

A matrix element is simply a matrix entry. Each element in a matrix is identified by naming the row and column in which it appears.
For example, consider matrix $G$:
$G=\left[\begin{array}{rrr}4& 14& -7\\ 18& 5& 13\\ -20& 4& 22\end{array}\right]$
The element ${g}_{2,1}$ is the entry in the $\text{second row}$ and the $\text{first column}$.
In this case ${g}_{2,1}=18$.
In general, the element in and of matrix $A$ is denoted as ${a}_{i,j}$.

${a}_{1,3}=$
5) $B=\left[\begin{array}{rr}12& -2.3\\ 4.6& 1.2& \end{array}\right]$
${b}_{2,1}=$
6) Matrix $C$ is a $2×3$ matrix with ${c}_{1,2}=6$.
Which could be matrix $C$?