Ecuaciones Matriciales

Ver explicación: Vídeo nº 2583 de CiberMatex

Dadas las matrices: A =
\left(
\begin{array}{cc}
1 & 1
\\ 3 & 4
\end{array}
\right)
 \qquad 
B =
\left(
\begin{array}{cc}
2 & 1
\\ 1 & 1
\end{array}
\right)
 \qquad 
C =
\left(
\begin{array}{cc}
1 & 2
\\ 3 & 3
\end{array}
\right)
Resuelve la siguiente ecuación matricial: - AX + BX = C

SOLUCIÓN

AX + BX = C
(A + B)X = C
(A+B)^{-1}(A + B)X = (A+B)^{-1} C
I \cdot X = (A+B)^{-1} C
 X = (A+B)^{-1} C

A+B =
\left(
\begin{array}{cc}
3 & 2
\\ 4 & 5
\end{array}
\right)

(A+B)^{-1} =
\left(
\begin{array}{cc}
5/7 & -2/7
\\ -4/7 & 3/7
\end{array}
\right)

X = (A+B)^{-1} \cdot C=
\left(
\begin{array}{cc}
5/7 & -2/7
\\ -4/7 & 3/7
\end{array}
\right)
\cdot \left(
\begin{array}{cc}
1 & 2
\\ 3 & 3
\end{array}
\right) = \fbox{\left(
\begin{array}{cc}
-1/7 & 4/7
\\ 5/7 & 1/7
\end{array}
\right)}