Equations with singular matrices

Task number: 2430

Solve the equation \(\mathbf A\mathbf X=\mathbf B\) for matrices:

  • Variant 1

    \(\mathbf A= \begin{pmatrix} 1 &0 &1\\ 3 &0 &2\\ 2 &2 &0\\ 0 &2 &2 \end{pmatrix} \), \( \mathbf B= \begin{pmatrix} 3 &-1\\ 8 &-3\\ 10 & 0\\ 8 & 2 \end{pmatrix} \).

  • Variant 2

    \(\mathbf A= \begin{pmatrix} 1 &0 &1\\ 3 &0 &3\\ 2 &2 &0\\ 0 &2 &2 \end{pmatrix} \), \( \mathbf B= \begin{pmatrix} 3 &-1\\ 8 &-3\\ 10 & 0\\ 8 & 2 \end{pmatrix} \).

  • Variant 3

    \( \begin{pmatrix} 1 &0 &1\\ 3 &0 &3\\ 2 &-1 &0\\ 0 &1 &2 \end{pmatrix} \), \( \mathbf B= \begin{pmatrix} 3 &-1\\ 9 &-3\\ 1 &-3\\ 5 & 1 \end{pmatrix} \).

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