Systems II.

Task number: 2384

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

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

Difficulty level: Easy task (using definitions and simple reasoning)
Solution require uncommon idea
Cs translation
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