# Lesson 7.3: Matrices

## Symbols

$[\phantom{\rule{.3em}{0ex}}\text{enlarged bracket, opening}$

⠠⠨⠣

$]\phantom{\rule{.3em}{0ex}}\text{enlarged bracket, closing}$

⠠⠨⠜

$\{\phantom{\rule{.3em}{0ex}}\text{enlarged brace, opening}$

⠠⠸⠣

$\}\phantom{\rule{.3em}{0ex}}\text{enlarged brace, closing}$

⠠⠸⠜

$(\phantom{\rule{.3em}{0ex}}\text{enlarged parenthesis, opening}$

⠠⠐⠣

$)\phantom{\rule{.3em}{0ex}}\text{enlarged parenthesis, closing}$

⠠⠐⠜

$|\phantom{\rule{.3em}{0ex}}\text{enlarged vertical bar}$

⠠⠸⠳

## Explanation

A matrix is a rectangular array of values organized in a table format of rows and columns. Items within a matrix are referred to as elements or entries. Matrices are typically enclosed within enlarged brackets, parenthesis, and/or vertical bars. The enlarged version of a grouping symbol (bracket, brace, parenthesis, vertical bar) is formed with the usual grouping symbol preceded by a dot six. For example, the opening enlarged bracket is dot six, dots four six, dots one two six and the closing enlarged bracket is dot six, dots four six, dots three four five.

In braille each row of the matrix begins with the enlarged opening grouping symbol and ends with the enlarged closing grouping symbol. The enlarged grouping symbols must be aligned vertically, with the columns left adjusted. One column of blank spaces should be left between columns of the matrix. Any values appearing outside of the grouping symbols must appear on the top line of the expression even though it may be centered to the overall expression in print.

### Example 1

$\left[\begin{array}{cc}3& 8\\ 4& 6\end{array}\right]$

⠠⠨⠣⠼⠉⠀⠼⠓⠠⠨⠜

⠠⠨⠣⠼⠙⠀⠼⠋⠠⠨⠜

### Example 2

$V=7\left[\begin{array}{cc}7& 8\\ 7& 6\end{array}\right]$

⠰⠠⠧⠀⠐⠶⠀⠼⠛⠀⠠⠨⠣⠼⠛⠀⠼⠓⠠⠨⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠣⠼⠛⠀⠼⠋⠠⠨⠜

If a signed numeral is included in the matrix, the placement of the values in columns should be adjusted for the minus sign to stand out.

### Example 3

$\left(\begin{array}{cc}8& 0\\ 8& -4\end{array}\right)$

⠠⠐⠣⠼⠓⠀⠀⠀⠼⠚⠠⠐⠜

⠠⠐⠣⠼⠓⠀⠐⠤⠼⠙⠠⠐⠜

### Example 4

$B=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

⠰⠠⠃⠀⠐⠶⠀⠠⠨⠣⠼⠁⠀⠼⠃⠀⠼⠉⠠⠨⠜

⠀⠀⠀⠀⠀⠀⠀⠠⠨⠣⠼⠙⠀⠼⠑⠀⠼⠋⠠⠨⠜

⠀⠀⠀⠀⠀⠀⠀⠠⠨⠣⠼⠛⠀⠼⠓⠀⠼⠊⠠⠨⠜

### Example 5

$\text{Find}\phantom{\rule{.3em}{0ex}}2\left[\begin{array}{ccc}2& -4& 1\\ 0& 2& -7\end{array}\right]$

⠠⠋⠔⠙⠀⠼⠃⠀⠠⠨⠣⠼⠃⠀⠐⠤⠼⠙⠀⠀⠀⠼⠁⠠⠨⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠣⠼⠚⠀⠀⠀⠼⠃⠀⠐⠤⠼⠛⠠⠨⠜

### Example 6

$\left|\begin{array}{cc}6& -4\\ 0& 2\end{array}\right|$

⠠⠸⠳⠼⠋⠀⠐⠤⠼⠙⠠⠸⠳

⠠⠸⠳⠼⠚⠀⠀⠀⠼⠃⠠⠸⠳

### Example 7

$\left[\begin{array}{ccc}1& x& -4\\ 2& 0& 5\end{array}\right]$

⠠⠨⠣⠼⠁⠀⠰⠭⠀⠐⠤⠼⠙⠠⠨⠜

⠠⠨⠣⠼⠃⠀⠼⠚⠀⠀⠀⠼⠑⠠⠨⠜