Cramer rule

Task number: 2605

By using Cramer rule solve the following systems of equations:

  • Variant 1

    \(\mathbf A\mathbf x=\mathbf b\) over \(\mathbb R\) for

    \( \mathbf A= \begin{pmatrix} 1 & 2 & -2 & 2 \\ 2 & 3 & 1 & 1 \\ -1 & 2 & 3 & -1 \\ 1 & -1 & 1 & -1 \\ \end{pmatrix} \) and \( \mathbf b = \begin{pmatrix} -2 \\ 2 \\ -1 \\ 4 \end{pmatrix} \).

  • Variant 2

    over \(\mathbb Z_5\):

    \[\begin{eqnarray*} 2x + y + 4z &=& 1 \\ 3x + y + 4z &=& 2 \\ 2x + 4y + 2z &=& 3 \end{eqnarray*}\]

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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