Editing Openai/695dfc16-b2ac-8005-980b-b86d96450929 (section)

===== 步驟 3：計算 ABCR =====

ABCR=A⋅B⋅A−1⋅RABCR = A·B·A^{-1}·RABCR=A⋅B⋅A−1⋅R
先計算 A−1RA^{-1} RA−1R：

A−1R=[−2.51.52−1][114514]=[−2.5∗114+1.5∗5142∗114−1∗514]=[−285+771228−514]=[486−286]A^{-1}R = 
\begin{bmatrix}-2.5 & 1.5\\2 & -1\end{bmatrix} \begin{bmatrix}114\\514\end{bmatrix} =
\begin{bmatrix}-2.5''114 +1.5''514\\ 2''114 -1''514\end{bmatrix} =
\begin{bmatrix}-285 +771\\228-514\end{bmatrix} =
\begin{bmatrix}486\\ -286\end{bmatrix}A−1R=[−2.521.5−1][114514]=[−2.5∗114+1.5∗5142∗114−1∗514]=[−285+771228−514]=[486−286]