a)

Zgodnie z wzorami obliczmy wyznaczniki.

$$\begin{gathered} W=\left|\begin{array}{cc}2& -1\\ 1& -1\end{array}\right|=2\cdot \left(-1\right)-\left(-1\right)\cdot 1=-2+1=-1 \\ {W}_x=\left|\begin{array}{cc}2& -1\\ -1& -1\end{array}\right|=2\cdot \left(-1\right)-\left(-1\right)\cdot (-1)=-2-1=-3 \\ {W}_y=\left|\begin{array}{cc}2& 2\\ 1& -1\end{array}\right|=2\cdot \left(-1\right)-2\cdot 1=-2-2=-4 \end{gathered}$$

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b)

Zgodnie z wzorami obliczmy wyznaczniki.

$$\begin{gathered} W=\left|\begin{array}{cc}4& 3\\ 1& -2\end{array}\right|=4\cdot \left(-2\right)-3\cdot 1=-8-3=-11 \\ {W}_x=\left|\begin{array}{cc}0& 3\\ 3& -2\end{array}\right|=0\cdot \left(-2\right)-3\cdot 3=-9 \\ {W}_y=\left|\begin{array}{cc}4& 0\\ 1& 3\end{array}\right|=4\cdot 3-0\cdot 1=12 \end{gathered}$$

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c)

Zgodnie z wzorami obliczmy wyznaczniki.

$$\begin{gathered} W=\left|\begin{array}{cc}\sqrt{2}& 1\\ 1& -\sqrt{2}\end{array}\right|=\sqrt{2}\cdot \left(-\sqrt{2}\right)-1\cdot 1=-2-1=-3 \\ {W}_x=\left|\begin{array}{cc}1-\sqrt{2}& 1\\ \sqrt{2}& -\sqrt{2}\end{array}\right|=\left(1-\sqrt{2}\right)\cdot (-\sqrt{2})-1\cdot \sqrt{2}=-\sqrt{2}+2-\sqrt{2}=2-2\sqrt{2} \\ {W}_y=\left|\begin{array}{cc}\sqrt{2}& 1-\sqrt{2}\\ 1& \sqrt{2}\end{array}\right|=\sqrt{2}\cdot \sqrt{2}-\left(1-\sqrt{2}\right)\cdot 1=2-1+\sqrt{2}=1+\sqrt{2} \end{gathered}$$