\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}

\begin{pmatrix}1&2\\3&4\\ \end{pmatrix}

\begin{bmatrix}1&2\\3&4\\ \end{bmatrix}

\begin{Bmatrix}1&2\\3&4\\ \end{Bmatrix}

\begin{vmatrix}1&2\\3&4\\ \end{vmatrix}

\begin{Vmatrix}1&2\\3&4\\ \end{Vmatrix}

\begin{pmatrix}
 1 & a_1 & a_1^2 & \cdots & a_1^n \\
 1 & a_2 & a_2^2 & \cdots & a_2^n \\
 \vdots  & \vdots& \vdots & \ddots & \vdots \\
 1 & a_m & a_m^2 & \cdots & a_m^n    
 \end{pmatrix}

\left[
\begin{array}{cc|c}
  1&2&3\\
  4&5&6
\end{array}
\right]

\begin{pmatrix}
    a & b\\
    c & d\\
  \hline
    1 & 0\\
    0 & 1
  \end{pmatrix}

\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)

\begin{equation}\begin{aligned}
\sqrt{37} &=\sqrt{\frac{73^{2}-1}{12^{2}}} \\
&=\sqrt{\frac{73^{2}}{12^{2}} \cdot \frac{73^{2}-1}{73^{2}}} \\
&=\sqrt{\frac{73^{2}}{12^{2}}} \sqrt{\frac{73^{2}-1}{73^{2}}} \\
&=\frac{73}{12} \sqrt{1-\frac{1}{73^{2}}} \\
& \approx \frac{73}{12}\left(1-\frac{1}{2 \cdot 73^{2}}\right)
\end{aligned}\end{equation}

\begin{aligned}
f(x) &=\left(x^{3}\right)+\left(x^{3}+x^{2}+x^{1}\right)+\left(x^{3}+x\right) \\
f^{\prime}(x) &=\left(3 x^{2}+2 x+1\right)+\left(3 x^{2}+2 x\right) \\
f^{\prime \prime}(x) &=(6 x+2)
\end{aligned}

f(n) =
\begin{cases}
n/2,  & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}

\left.
\begin{array}{l}
\text{if $n$ is even:}&n/2\\
\text{if $n$ is odd:}&3n+1
\end{array}
\right\}
=f(n)

f(n) =
\begin{cases}
\frac{n}{2},  & \text{if $n$ is even} \\[2ex]
3n+1, & \text{if $n$ is odd}
\end{cases}

\begin{array}{c|lcr}
n & \text{Left} & \text{Center} & \text{Right} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}

% outer vertical array of arrays
\begin{array}{c}
% inner horizontal array of arrays
\begin{array}{cc}
% inner array of minimum values
\begin{array}{c|cccc}
\text{min} & 0 & 1 & 2 & 3\\
\hline
0 & 0 & 0 & 0 & 0\\
1 & 0 & 1 & 1 & 1\\
2 & 0 & 1 & 2 & 2\\
3 & 0 & 1 & 2 & 3
\end{array}
&
% inner array of maximum values
\begin{array}{c|cccc}
\text{max}&0&1&2&3\\
\hline
0 & 0 & 1 & 2 & 3\\
1 & 1 & 1 & 2 & 3\\
2 & 2 & 2 & 2 & 3\\
3 & 3 & 3 & 3 & 3
\end{array}
\end{array}
\\
% inner array of delta values
\begin{array}{c|cccc}
\Delta&0&1&2&3\\
\hline
0 & 0 & 1 & 2 & 3\\
1 & 1 & 0 & 1 & 2\\
2 & 2 & 1 & 0 & 1\\
3 & 3 & 2 & 1 & 0
\end{array}
\end{array}

\left\{ 
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\ 
a_2x+b_2y+c_2z=d_2 \\ 
a_3x+b_3y+c_3z=d_3
\end{array}
\right.

\begin{cases}
a_1x+b_1y+c_1z=d_1 \\ 
a_2x+b_2y+c_2z=d_2 \\ 
a_3x+b_3y+c_3z=d_3
\end{cases}

\left\{
\begin{aligned} 
a_1x+b_1y+c_1z &=d_1+e_1 \\ 
a_2x+b_2y&=d_2 \\ 
a_3x+b_3y+c_3z &=d_3 
\end{aligned} 
\right.

\left\{
\begin{array}{ll}
a_1x+b_1y+c_1z &=d_1+e_1 \\ 
a_2x+b_2y &=d_2 \\ 
a_3x+b_3y+c_3z &=d_3 
\end{array} 
\right.

\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex] 
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex] 
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}

\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}

\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ & \color{black}{text} \\
\verb+\color{gray}{text}+ & \color{gray}{text} \\
\verb+\color{silver}{text}+ & \color{silver}{text} \\
\verb+\color{white}{text}+ & \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ & \color{maroon}{text} \\
\verb+\color{red}{text}+ & \color{red}{text} \\
\verb+\color{yellow}{text}+ & \color{yellow}{text} \\
\verb+\color{lime}{text}+ & \color{lime}{text} \\
\verb+\color{olive}{text}+ & \color{olive}{text} \\
\verb+\color{green}{text}+ & \color{green}{text} \\
\verb+\color{teal}{text}+ & \color{teal}{text} \\
\verb+\color{aqua}{text}+ & \color{aqua}{text} \\
\verb+\color{blue}{text}+ & \color{blue}{text} \\
\verb+\color{navy}{text}+ & \color{navy}{text} \\
\verb+\color{purple}{text}+ & \color{purple}{text} \\ 
\verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\
\hline
\end{array}

\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ & \color{black}{text} \\
\verb+\color{gray}{text}+ & \color{gray}{text} \\
\verb+\color{silver}{text}+ & \color{silver}{text} \\
\verb+\color{white}{text}+ & \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ & \color{maroon}{text} \\
\verb+\color{red}{text}+ & \color{red}{text} \\
\verb+\color{yellow}{text}+ & \color{yellow}{text} \\
\verb+\color{lime}{text}+ & \color{lime}{text} \\
\verb+\color{olive}{text}+ & \color{olive}{text} \\
\verb+\color{green}{text}+ & \color{green}{text} \\
\verb+\color{teal}{text}+ & \color{teal}{text} \\
\verb+\color{aqua}{text}+ & \color{aqua}{text} \\
\verb+\color{blue}{text}+ & \color{blue}{text} \\
\verb+\color{navy}{text}+ & \color{navy}{text} \\
\verb+\color{purple}{text}+ & \color{purple}{text} \\ 
\verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\
\hline
\end{array}

f\left(
   \left[ 
     \frac{
       1+\left\{x,y\right\}
     }{
       \left(
          \frac{x}{y}+\frac{y}{x}
       \right)
       \left(u+1\right)
     }+a
   \right]^{3/2}
\right)

\begin{aligned}
a=&\left(1+2+3+  \cdots \right. \\
& \cdots+ \left. \infty-2+\infty-1+\infty\right)
\end{aligned}

\left\langle  
  q
\middle\|
  \frac{\frac{x}{y}}{\frac{u}{v}}
\middle| 
   p 
\right\rangle

\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit
\color{red}{\heartsuit}\quad\color{red}{\diamondsuit}

♠\quad♡\quad♢\quad♣\\
♤\quad♥\quad♦\quad♧

\begin{array}{c|rrrr}& x^3 & x^2 & x^1 &  x^0\\ & 1 & -6 & 11 & -6\\ {\color{red}1} & \downarrow & 1 & -5 & 6\\ \hline & 1 & -5 & 6 & |\phantom{-} {\color{blue}0} \end{array}

x^3−6x^2+11x−6=(x−{\color{red}1})(x^2−5x+6)+{\color{blue}0}

\text{45^\text{o}

\sum_{n=1}^\infty \frac{1}{n^2} \to
  \textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to
  \displaystyle \sum_{n=1}^\infty \frac{1}{n^2}

e=m c^{2}

\begin{aligned}
a &=b+c \\
&=d+e+f+g \\
&=h+i
\end{aligned}

\begin{array}{l}
a=b+c \\
x=y z \\
l=m-n
\end{array}

54\,321.123\,45

\left.\mathrm{m}\middle/\mathrm{s}^2\right.

\mu_0=4\pi\times10^{-7} \ \left.\mathrm{\mathrm{T}\!\cdot\!\mathrm{m}}\middle/\mathrm{A}\right.

\begin{array}{rrrrrr|r}
           & x_1 & x_2 & s_1 & s_2 & s_3 &    \\ \hline
       s_1 &   0 &   1 &   1 &   0 &   0 &  8 \\
       s_2 &   1 &  -1 &   0 &   1 &   0 &  4 \\
       s_3 &   1 &   1 &   0 &   0 &   1 & 12 \\ \hline
           &  -1 &  -1 &   0 &   0 &   0 &  0
\end{array}

\begin{array}{rrrrrrr|rr}
  & x_1 & x_2 & s_1 & s_2 & s_3 &  w &    & \text{ratio} \\ \hline
  s_1 &   0 &   1 &   1 &   0 &   0 &  0 &  8 &            - \\
w & 1^* &  -1 &   0 &  -1 &   0 &  1 &  4 &            4 \\
  s_3 &   1 &   1 &   0 &   0 &   1 &  0 & 12 &           12 \\ \hdashline
  &   1 &  -1 &   0 &  -1 &   0 &  0 &  4 &              \\ \hline
  s_1 &   0 &   1 &   1 &   0 &   0 &  0 &  8 &              \\
  x_1 &   1 &  -1 &   0 &  -1 &   0 &  1 &  4 &              \\
  s_3 &   0 &   2 &   0 &   2 &   1 & -1 &  8 &              \\ \hdashline
  &   0 &   0 &   0 &   0 &   0 & -1 &  0 &
\end{array}

\begin{array}{rrrrrrrr|r}
         & x_1 & x_2 & x_3 & x_4 & x_5 & x_6 &  x_7 &        \\ \hline
     x_4 &   0 &  -3 &   7 &   1 &   0 &   0 &    2 & 2M  -4 \\
     x_5 &   0 &  -9 &   0 &   0 &   1 &   0 &   -1 & -M  -3 \\
     x_6 &   0 &   6 &  -1 &   0 &   0 &   1 & -4^* & -4M +8 \\
     x_1 &   1 &   0 &   1 &   0 &   0 &   0 &    1 &      M \\ \hline
         &   0 &   1 &   1 &   0 &   0 &   0 &    2 &     2M \\
\text{ratio} &     &     &   1 &     &     &     &  1/2 &
\end{array}

\begin{array}{rrrrrrr|r}
         &  x_1 &  x_2 &  x_3 &  s_1 &    s_2 &  s_3 &       \\     \hline
     s_1 &   -2 &    0 &   -2 &    1 &      0 &    0 &   -60 \\
     s_2 &   -2 & -4^* &   -5 &    0 &      1 &    0 &   -70 \\
     s_3 &    0 &   -3 &   -1 &    0 &      0 &    1 &   -27 \\ \hdashline
         &    8 &   10 &   25 &    0 &      0 &    0 &     0 \\
\text{ratio} &   -4 & -5/2 &   -5 &      &        &      &       \\     \hline
     s_1 & -2^* &    0 &   -2 &    1 &      0 &    0 &   -60 \\
     x_2 &  1/2 &    1 &  5/4 &    0 &   -1/4 &    0 &  35/2 \\
     s_3 &  3/2 &    0 & 11/4 &    0 &   -3/4 &    1 &  51/2 \\ \hdashline
         &    3 &    0 & 25/2 &    0 &    5/2 &    0 &  -175 \\
\text{ratio} & -3/2 &      & 25/4 &      &        &      &       \\     \hline
     x_1 &    1 &    0 &    1 & -1/2 &      0 &    0 &    30 \\
     x_2 &    0 &    1 &  3/4 &  1/4 &   -1/4 &    0 &   5/2 \\
     s_3 &    0 &    0 &  5/4 &  3/4 & -3/4^* &    1 & -39/2 \\ \hdashline
         &    0 &    0 & 19/2 &  3/2 &    5/2 &    0 &  -265 \\
\text{ratio} &      &      &      &      &  \dots &      &       \\     \hline
     x_1 &    1 &    0 &    1 & -1/2 &      0 &    0 &    30 \\
     x_2 &    0 &    1 &  1/3 &    0 &      0 & -1/3 &     9 \\
     s_2 &    0 &    0 & -5/3 &   -1 &      1 & -4/3 &    26 \\ \hdashline
         &    0 &    0 & 41/3 &    4 &      0 & 10/3 &  -330
\end{array}

\Large\LaTeX

\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}

\Biggl(\biggl(\Bigl(\bigl((egg)\bigr)\Bigr)\biggr)\Biggr)

\mathbb{CHNQRZ}

\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

\mathbf{abcdefghijklmnopqrstuvwxyz}

\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

\mathit{abcdefghijklmnopqrstuvwxyz}

\pmb{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}

\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}