Matemática, perguntado por Jennifersouza, 11 meses atrás

No sistema matricial dado por {x+y=3A}                                                                                                                             {x-y=2B}  onde A= [2 0] e B= [1 5], os determinantes das matrizes x e y serão, respectivamente :               [0 4]         [3 0]                                                  a) 9, -4 b) -4, 9 c) -3,-9 d) 9,-3 e) -9, -3               


adrielcavalcant: oi =)
Jennifersouza: oii

Soluções para a tarefa

Respondido por Niiya
20
X + Y = 3*\left[\begin{array}{cc}2&0\\0&4\end{array}\right]
X + Y = \left[\begin{array}{cc}6&0\\0&12\end{array}\right]

X - Y = 2*\left[\begin{array}{cc}1&5\\3&0\end{array}\right]
X - Y = \left[\begin{array}{cc}2&10\\6&0\end{array}\right]
____________________

X + Y = \left[\begin{array}{cc}6&0\\0&12\end{array}\right]
X - Y = \left[\begin{array}{cc}2&10\\6&0\end{array}\right]

Somando as equações:

X+X+Y-Y=\left[\begin{array}{cc}6&0\\0&12\end{array}\right]+\left[\begin{array}{cc}2&10\\6&0\end{array}\right]
2X=\left[\begin{array}{cc}8&10\\6&12\end{array}\right]
X=\left[\begin{array}{cc}4&5\\3&6\end{array}\right]


X + Y = \left[\begin{array}{cc}6&0\\0&12\end{array}\right]
\left[\begin{array}{cc}4&5\\3&6\end{array}\right]+Y=\left[\begin{array}{cc}6&0\\0&12\end{array}\right]
Y=\left[\begin{array}{cc}6&0\\0&12\end{array}\right]-\left[\begin{array}{cc}4&5\\3&6\end{array}\right]
Y=\left[\begin{array}{cc}2&-5\\-3&6\end{array}\right]
____________________

det X = det\left[\begin{array}{cc}4&5\\3&6\end{array}\right]=(4*6)-(5*3)=24-15=9
detY=det\left[\begin{array}{cc}2&-5\\-3&6\end{array}\right]=(2*6)-([-5]*[-3])=12-15=-3

Letra D)
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