Megoldás - Mátrix alapműveletek

$$\in v\left(\left[\begin{array}{cc}-2& 5\\ 5& 2\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvPlan

$$\in v\left(\left[\begin{array}{cc}-2& 5\\ 5& 2\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvCheck

$$\in v\left(\left[\begin{array}{cc}-2& 5\\ 5& 2\end{array}\right]\right)$$

R1 <-> R2

$$\left[\begin{array}{cccc}5& 2& 0& 1\\ -2& 5& 1& 0\end{array}\right]$$

R1 <- 1/5R1

$$\left[\begin{array}{cccc}1& 0.4& 0& 0.2\\ -2& 5& 1& 0\end{array}\right]$$

R2 <- R2 + 2R1

$$\left[\begin{array}{cccc}1& 0.4& 0& 0.2\\ 0& 5.8& 1& 0.4\end{array}\right]$$

R2 <- 5/29R2

$$\left[\begin{array}{cccc}1& 0.4& 0& 0.2\\ 0& 1& 0.172414& 0.068966\end{array}\right]$$

R1 <- R1 - 2/5R2

$$\left[\begin{array}{cccc}1& 0& -0.068966& 0.172414\\ 0& 1& 0.172414& 0.068966\end{array}\right]$$

MatrixCoreOperationsStep2TextUnitInv

$$\left[\begin{array}{cccc}-0& 068966& 0& 172414\\ 0& 172414& 0& 068966\end{array}\right]$$

MatrixCoreOperationsStep3TransitionConclusionInv

$$\left[\begin{array}{cccc}-0& 068966& 0& 172414\\ 0& 172414& 0& 068966\end{array}\right]$$

MatrixCoreOperationsStep3TransitionStudyTipInv

$$\left[\begin{array}{cccc}-0& 068966& 0& 172414\\ 0& 172414& 0& 068966\end{array}\right]$$

Mutasd be a végső mátrix- vagy skaláreredményt kanonikus alakban a stabil útválasztás és ellenőrzés érdekében.