Ensino Superior ⇒ (Algebra linear) Determine as matrizes x e y tais que Tópico resolvido

[thetruth]

[tex3]sendo \ A\begin{pmatrix}
9 & 4 & 12 \\
6 & 12 & 11\\
\end{pmatrix}[/tex3]

[tex3]e\ B\begin{pmatrix}
-8 & 7 & -9 \\
-12& -19& -2 \\
\end{pmatrix}[/tex3]

determine as matrizes x e y tais que [tex3]\begin{cases}
2x+y=A \\
x+y=B
\end{cases}[/tex3]

[deOliveira]

[tex3]A=\begin{pmatrix}9 & 4 & 12 \\6 & 12 & 11\\\end{pmatrix}\\B=\begin{pmatrix}-8 & 7 & -9 \\-12& -19& -2 \\\end{pmatrix}[/tex3]
[tex3]\begin{cases}
2x+y=A \ \ (I)\\
x+y=B\ \ \ (II)
\end{cases}[/tex3]

Fazendo [tex3](I)-(II)[/tex3] teremos:
[tex3]2x+y-(x+y)=A-B\\\implies x=A-B\\\therefore x=\begin{pmatrix}17&-3&21\\18&31&13\end{pmatrix}[/tex3]

De [tex3](II)[/tex3] temos:
[tex3]x+y=B\\\implies y=B-x\\\therefore y=\begin{pmatrix}-25&47&-30\\-30&-50&-15\end{pmatrix}[/tex3]

Espero ter ajudado.