Megoldás - Mátrix alapműveletek

$$\in v\left(\left[\begin{array}{cc}4& 5\\ 5& -1\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvPlan

$$\in v\left(\left[\begin{array}{cc}4& 5\\ 5& -1\end{array}\right]\right)$$

MatrixCoreOperationsStep2TransitionInvCheck

$$\in v\left(\left[\begin{array}{cc}4& 5\\ 5& -1\end{array}\right]\right)$$

R1 <-> R2

$$\left[\begin{array}{cccc}5& -1& 0& 1\\ 4& 5& 1& 0\end{array}\right]$$

R1 <- 1/5R1

$$\left[\begin{array}{cccc}1& -0.2& 0& 0.2\\ 4& 5& 1& 0\end{array}\right]$$

R2 <- R2 - 4R1

$$\left[\begin{array}{cccc}1& -0.2& 0& 0.2\\ 0& 5.8& 1& -0.8\end{array}\right]$$

R2 <- 5/29R2

$$\left[\begin{array}{cccc}1& -0.2& 0& 0.2\\ 0& 1& 0.172414& -0.137931\end{array}\right]$$

R1 <- R1 + 1/5R2

$$\left[\begin{array}{cccc}1& 0& 0.034483& 0.172414\\ 0& 1& 0.172414& -0.137931\end{array}\right]$$

MatrixCoreOperationsStep2TextUnitInv

$$\left[\begin{array}{cccc}0& 034483& 0& 172414\\ 0& 172414& -0& 137931\end{array}\right]$$

MatrixCoreOperationsStep3TransitionConclusionInv

$$\left[\begin{array}{cccc}0& 034483& 0& 172414\\ 0& 172414& -0& 137931\end{array}\right]$$

MatrixCoreOperationsStep3TransitionStudyTipInv

$$\left[\begin{array}{cccc}0& 034483& 0& 172414\\ 0& 172414& -0& 137931\end{array}\right]$$

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