Title: Example Content LaTeX

Simple text example

\(A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} B_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix}\)

Fill in the blanks example

Fill in the blanks

Q: \(M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & X & \frac{1}{6} \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}\)

Which number should replace "X"? [...]
A: 0

Drag and Drop example

Drag numbers to correct places inside the matrix

- \(\begin{bmatrix}   & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & 0 &   \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}\)
- $$\frac{5}{6}$$
- $$\frac{1}{6} $$
Q: 1
A: $$\frac{5}{6}$$
Q: 2
A: $$\frac{1}{6} $$

Course presentation example

test latex

$$\frac{ \begin{array}[b]{r} \left( x_1 x_2 \right)\\ \times \left( x'_1 x'_2 \right) \end{array} }{ \left( y_1y_2y_3y_4 \right) }$$

$$\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x$$

$$ \boldsymbol{\beta} = (\beta_1,\beta_2,\dotsc,\beta_n) $$

$$f(n) = n^5 + 4n^2 + 2 |_{n=17} $$

$$ \sqrt[n]{1+x+x^2+x^3+\dots+x^n} $$

$$\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}dx$$

- \(\sqrt[n]{1+x+x^2+x^3+\dots+x^n} \)
- \(\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x \)
Q: Root example
A: \(\sqrt[n]{1+x+x^2+x^3+\dots+x^n} \)
Q: Integral example
A: \(\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x \)

Fill in the blanks

Q: \(M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & X & \frac{1}{6} \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}\)

Which number should replace "X"? [...]
A: 0

$$A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix}$$

$$M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & 0 & \frac{1}{6} \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}$$

\[ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ -(n+1)/2 & \quad \text{if } n \text{ is odd} \end{cases} \]

True/False example

Q: Is this correct \( \sqrt{16}=4 \)
A: true

Multiple choice example

Q: Which one is a root example?
- \( \boldsymbol{\beta} = (\beta_1,\beta_2,\dotsc,\beta_n) \)
- \( f(n) = n^5 + 4n^2 + 2 |_{n=17} \)
- \( \sqrt[n]{1+x+x^2+x^3+\dots+x^n} \) (correct)

All formulas used in this example are taken from https://en.wikibooks.org/wiki/LaTeX/Mathematics