Ecuaciones Matriciales

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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)}