## Matrices of order 5

### Task number: 2598

Calculate determinants of the following real matrices:

• #### Variant 1

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

• #### Variant 2

$$\begin{pmatrix} 1 & 2 & 0 & 2 & -1 \\ 0 & 1 & 3 & -1 & 0 \\ 1 & 2 & 0 & 2 & 1 \\ 0 & -1 & 3 & 1 & 0 \\ -1 & 2 & 0 & 2 & 1 \\ \end{pmatrix}$$

• #### Variant 3

$$\begin{pmatrix} 1 & -1 & 1 & 1 & 3 \\ 0 & 2 & 1 & 0 & -1 \\ 2 & -1 & 1 & -3 & 0 \\ 0 & 0 & -1 & 2 & 1 \\ 3 & 2 & 0 & 1 & 0 \\ \end{pmatrix}$$

• #### Variant 4

$$\begin{pmatrix} 0 & 0 & 1 & 2 & 3 \\ 0 & 1 & 2 & 3 & 2 \\ 1 & 2 & 3 & 2 & 1 \\ 2 & 3 & 2 & 1 & 0 \\ 3 & 2 & 1 & 0 & 0 \\ \end{pmatrix}$$

• #### Variant 5

$$\begin{pmatrix} 1 & 1 & -1 & 1 & 1 \\ -1 & 1 & 1 & 1 & -1 \\ 1 & -1 & 1 & 1 & 1 \\ 1 & -1 & 1 & 1 & -1 \\ -1 & 1 & 1 & -1 & 1 \\ \end{pmatrix}$$

• #### Variant 6

$$\begin{pmatrix} 2 & 0 & 2 & 0 & -2 \\ 0 & 3 & 0 & 2 & 0 \\ 2 & 0 & -2 & 0 & 2 \\ 0 & 2 & 0 & 3 & 0 \\ -2 & 0 & 2 & 0 & 2 \\ \end{pmatrix}$$