matrix

in mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, with elements arranged in rows and columns

the size of a matrix is defined by the number of rows and columns it contains
a matrix with $m$ rows and $n$ columns is called a m-by-n matrix

matrices with a single row are called row vectors, and those with a single column are called column vectors

notation

A matrix can use square brackets or normal brackets.

$\mathbf{A}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]$

matrix addition

matrix addition is the operation of adding two matrices of the same order

we add the corresponding entries together

matrix multiplication

matrix multiplication is the operation of multiplying two matrices with a column size matching with a row size, and a row size matching with a column size

determinant

$\mathbf{A}=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$
$\det (\mathbf{A})=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$
$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=a\cdot d-c\cdot b$

You can check how to calculate the determinant of a 3 by 3 matrix online.