Cramer sin reegel

Cramer sin reegel as en metood, am linear liknangsüsteemen tu liasin. Hat as näämd efter Gabriel Cramer.

Bispal

(1) Det liknangsüsteem uun normoolfurem

$\begin{array}{c}1x_1+2x_2=3\\ 4x_1+5x_2=6\end{array}$

(2) Det ütjwidjet koefisientenmaatriks

$\left(\begin{array}{cc}A& b\end{array}\right)=\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right)$

(3) Liasang efter Cramer sin reegel (det=determinant)

$x_1=\frac{\det (A_1)}{\det (A)}=\frac{\det \left(\begin{array}{cc}3& 2\\ 6& 5\end{array}\right)}{\det \left(\begin{array}{cc}1& 2\\ 4& 5\end{array}\right)}=\frac{3\cdot 5-6\cdot 2}{1\cdot 5-4\cdot 2}=\frac{3}{-3}=-1$

$x_2=\frac{\det (A_2)}{\det (A)}=\frac{\det \left(\begin{array}{cc}1& 3\\ 4& 6\end{array}\right)}{\det \left(\begin{array}{cc}1& 2\\ 4& 5\end{array}\right)}=\frac{1\cdot 6-4\cdot 3}{1\cdot 5-4\cdot 2}=\frac{-6}{-3}=2$

Luke uk diar

• Lineaar algebra