Matrix equations

Task number: 2427

For real matrices

\( \mathbf A= \begin{pmatrix} 1 & 0 & 1 & 1 \\ 2 & 0 & 1 & 1 \\ 2 & 1 & 0 & 0 \\ 1 & 2 & 1 & 0 \\ \end{pmatrix},\ \mathbf B= \begin{pmatrix} 0 & 2 & 2 & 1 \\ 1 & 0 & 2 & 0 \\ 2 & 1 & 0 & 2 \\ 2 & 2 & 1 & 1 \\ \end{pmatrix},\ \mathbf C= \begin{pmatrix} 2 & 0 & 1 & 0 \\ 1 & 2 & 0 & 1 \\ 2 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ \end{pmatrix},\ \)

\( \mathbf D= \begin{pmatrix} 1 & 1 & 0 & 0 \\ 1 & 2 & 1 & 1 \\ 1 & 1 & 2 & 0 \\ 0 & 1 & 2 & 1 \\ \end{pmatrix},\ \mathbf E= \begin{pmatrix} 1 & 1 & 2 & 0 \\ 1 & 2 & 1 & 1 \\ 0 & 1 & 2 & 1 \\ 1 & 2 & 0 & 0 \\ \end{pmatrix}\ \) solve equations:

  • Variant 1

    \((\mathbf A-\mathbf D)\mathbf X_1=\mathbf A\)

  • Variant 2

    \(\mathbf X_2\mathbf B=\mathbf C+\mathbf D\)

  • Variant 3

    \(\mathbf A\mathbf X^{-1}_3=\mathbf E^T\)

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