$\LaTeX$ Rendering Test:

Raw LaTeX:

$2x+2=5$

Rendered:

$2x+2=5$

Raw LaTeX:

$L_1=3x^2+2x+1$

Rendered:

$L_1=3x^2+2x+1$

Raw LaTeX:

\begin{bmatrix}
   a & b \\
   c & d
\end{bmatrix}

Rendered:

$$ \begin{bmatrix} a & b \\ c & d \end{bmatrix} $$

Raw LaTeX:

$$
\begin{align*}
y = y(x,t) &= A e^{i\theta} \\
&= A (\cos \theta + i \sin \theta) \\
&= A (\cos(kx - \omega t) + i \sin(kx - \omega t)) \\
&= A\cos(kx - \omega t) + i A\sin(kx - \omega t)  \\
&= A\cos \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) + i A\sin \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big)  \\
&= A\cos \frac{2\pi}{\lambda} (x - v t) + i A\sin \frac{2\pi}{\lambda} (x - v t)
\end{align*}
$$

Rendered:

$$ \begin{align*} y = y(x,t) &= A e^{i\theta} \\ &= A (\cos \theta + i \sin \theta) \\ &= A (\cos(kx - \omega t) + i \sin(kx - \omega t)) \\ &= A\cos(kx - \omega t) + i A\sin(kx - \omega t) \\ &= A\cos \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) + i A\sin \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) \\ &= A\cos \frac{2\pi}{\lambda} (x - v t) + i A\sin \frac{2\pi}{\lambda} (x - v t) \end{align*} $$