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## Algebra (all content)

### Unit 20: 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 start color #11accd, start text, t, w, o, space, r, o, w, s, end text, end color #11accd and start color #e07d10, start text, t, h, r, e, e, space, c, o, l, u, m, n, s, end text, end color #e07d10, we write its dimensions as start color #11accd, 2, end color #11accd, times, start color #e07d10, 3, end color #e07d10, pronounced "two by three".
In contrast, matrix B has start color #11accd, start text, t, h, r, e, e, space, r, o, w, s, end text, end color #11accd and start color #e07d10, start text, t, w, o, space, c, o, l, u, m, n, s, end text, end color #e07d10, so it is a start color #11accd, 3, end color #11accd, times, start color #e07d10, 2, end color #e07d10 matrix.
$B=\left[\begin{array}{rr}-8 & -4 \\ 23 & 12 \\18 &10 \end{array}\right]$
When working with matrix dimensions, remember start color #11accd, start text, r, o, w, s, end text, end color #11accd, times, start color #e07d10, start text, c, o, l, u, m, n, s, end text, end color #e07d10!

1) What are the dimensions of matrix D?
$D=\left[\begin{array}{rr}-7 & 24 &~~~~2 \\ 1 & 15 &~~11 \\-9 &12&~~~0 \\8 &-3&-1 \end{array}\right]$
times

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

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

## 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:
$G=\left[\begin{array}{rr}4& 14&-7 \\ 18 & 5&13 \\-20 &4&22 \end{array}\right]$
The element g, start subscript, start color #11accd, 2, end color #11accd, comma, start color #e07d10, 1, end color #e07d10, end subscript is the entry in the start color #11accd, start text, s, e, c, o, n, d, space, r, o, w, end text, end color #11accd and the start color #e07d10, start text, f, i, r, s, t, space, c, o, l, u, m, n, end text, end color #e07d10.
In this case g, start subscript, 2, comma, 1, end subscript, equals, start color #ca337c, 18, end color #ca337c.
In general, the element in start color #11accd, start text, r, o, w, space, end text, i, end color #11accd and start color #e07d10, start text, c, o, l, u, m, n, space, end text, j, end color #e07d10 of matrix A is denoted as a, start subscript, start color #11accd, i, end color #11accd, comma, start color #e07d10, j, end color #e07d10, end subscript.

4) $A=\left[\begin{array}{rr}2 & -4 &~~~8 \\ 1 & 5&-5 \\-2 &6&~~~2 \end{array}\right]$
5) $B=\left[\begin{array}{rr}12 & -2.3 \\ 4.6 & 1.2& \end{array}\right]$