# Matrices, vectors, and determinants

```latex
\mathbf{v}=\begin{pmatrix}v_1\\v_2\\v_3\end{pmatrix}
```

```latex
A=\begin{bmatrix}
a & b\\
c & d
\end{bmatrix}
```

```latex
\det(A)=\begin{vmatrix}
a & b\\
c & d
\end{vmatrix}=ad-bc
```

```latex
\begin{pmatrix}
\cos\theta & -\sin\theta\\
\sin\theta & \cos\theta
\end{pmatrix}
\begin{pmatrix}x\\y\end{pmatrix}
```

```latex
A^{-1}=\frac{1}{\det A}\operatorname{adj}(A)
```