LEMNISCATA
Matemàtiques
Sía $A=\begin{pmatrix}0&3&3\\0&-2&0\end{pmatrix}$ y $B=\begin{pmatrix}7&6&-1\\14&3&7\end{pmatrix}$ alavez lo sistema ye:
$$\left\{\begin{array}{rl}X-2Y&=A\\2X+3Y&=B\end{array}\right.$$
Multiplicamos per $2$ la primera equación:
$$\left\{\begin{array}{rl}2X-4Y&=2A\\2X+3Y&=B\end{array}\right.$$
Si a la equación segunda le restamos la primera obtenemos:
$$7Y=B-2A$$
d’an
$$Y=\dfrac17\cdot(B-2A)=\dfrac17\cdot\left[\begin{pmatrix}7&6&-1\\14&3&7\end{pmatrix}-2\begin{pmatrix}0&3&3\\0&-2&0\end{pmatrix}\right]~;\ Y=\dfrac17\cdot\begin{pmatrix}7&0&-7 \\4&7&7\end{pmatrix}~;\ \boxed{Y=\begin{pmatrix}1&0&-1\\2&1&1\end{pmatrix}}$$
Dau que $X-2Y=A$, alavez:
$$\begin{align}X=A+2Y=\begin{pmatrix}0&3&3\\0&-2&0\end{pmatrix}+2\begin{pmatrix}1&0&-1\\2&1&1\end{pmatrix}~;\\ \boxed{X=\begin{pmatrix}2&3&1\\4&0&2\end{pmatrix}}\end{align}$$