Megoldás - Mátrix alapműveletek

$$\in v\left(\left[\begin{array}{cc}-2& 4\\ 4& 1\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvPlan

$$\in v\left(\left[\begin{array}{cc}-2& 4\\ 4& 1\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvCheck

$$\in v\left(\left[\begin{array}{cc}-2& 4\\ 4& 1\end{array}\right]\right)$$

R1 <-> R2

$$\left[\begin{array}{cccc}4& 1& 0& 1\\ -2& 4& 1& 0\end{array}\right]$$

R1 <- 1/4R1

$$\left[\begin{array}{cccc}1& 0.25& 0& 0.25\\ -2& 4& 1& 0\end{array}\right]$$

R2 <- R2 + 2R1

$$\left[\begin{array}{cccc}1& 0.25& 0& 0.25\\ 0& 4.5& 1& 0.5\end{array}\right]$$

R2 <- 2/9R2

$$\left[\begin{array}{cccc}1& 0.25& 0& 0.25\\ 0& 1& 0.222222& 0.111111\end{array}\right]$$

R1 <- R1 - 1/4R2

$$\left[\begin{array}{cccc}1& 0& -0.055556& 0.222222\\ 0& 1& 0.222222& 0.111111\end{array}\right]$$

MatrixCoreOperationsStep2TextUnitInv

$$\left[\begin{array}{cccc}-0& 055556& 0& 222222\\ 0& 222222& 0& 111111\end{array}\right]$$

MatrixCoreOperationsStep3TransitionConclusionInv

$$\left[\begin{array}{cccc}-0& 055556& 0& 222222\\ 0& 222222& 0& 111111\end{array}\right]$$

MatrixCoreOperationsStep3TransitionStudyTipInv

$$\left[\begin{array}{cccc}-0& 055556& 0& 222222\\ 0& 222222& 0& 111111\end{array}\right]$$

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