## Systems II.

Find at least one nontrivial solution for the system $$\mathbf A\mathbf x=\mathbf 0$$ for the following matrix $$\mathbf A$$, if such solution exists.

• #### Variant 1

$$\mathbf A=\begin{pmatrix} 2 & 3 & 4 & 5 \\ 3 & 0 & 2 & -3 \\ 7 & 6 & 10 & 7 \\ \end{pmatrix}$$

• #### Variant 2

$$\mathbf A=\begin{pmatrix} 2 & -3 & 13 & 18 \\ 6 & -9 & 7 & 10 \\ 2 & -3 & -3 & -4 \\ \end{pmatrix}$$

• #### Variant 3

$$\mathbf A=\begin{pmatrix} 1 & 2 & -1 & 1 \\ 2 & -1 & 4 & 10 \\ 1 & 0 & 3 & -5 \\ 2 & 5 & 2 & 2 \\ \end{pmatrix},$$

• #### Variant 4

$$\mathbf A=\begin{pmatrix} 1 & -1 & 1 & 2 \\ 1 & 8 & 7 & -7 \\ 1 & 2 & 3 & -1 \\ 1 & 5 & 5 & -4 \\ \end{pmatrix}$$