Seja A=![\left[\begin{array}{cc}1&2\\0&-1\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B2%5C%5C0%26amp%3B-1%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{cc}1&2\\0&-1\\\end{array}\right]")
e B=![\left[\begin{array}{cc}-1&3\\2&-6\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26amp%3B3%5C%5C2%26amp%3B-6%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{cc}-1&3\\2&-6\\\end{array}\right]")
. Seja X uma matriz tal que 
. Determine X.
Soluções para a tarefa
Respondido por
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Seja ![X= \left[\begin{array}{cc}a&b\\c&d\end{array}\right]](https://tex.z-dn.net/?f=+X%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26amp%3Bb%5C%5Cc%26amp%3Bd%5Cend%7Barray%7D%5Cright%5D+ "X= \left[\begin{array}{cc}a&b\\c&d\end{array}\right]")
![XA= \left[\begin{array}{cc}1a+0b&2a-b\\c+0d&2c-d\end{array}\right] \\ \\
XA= \left[\begin{array}{cc}a&2a-b\\c&2c-d\end{array}\right] \\ \\
(XA)^t= \left[\begin{array}{cc}a&c\\2a-b&2c-d\end{array}\right] \\ \\](https://tex.z-dn.net/?f=XA%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1a%2B0b%26amp%3B2a-b%5C%5Cc%2B0d%26amp%3B2c-d%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C%0AXA%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26amp%3B2a-b%5C%5Cc%26amp%3B2c-d%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C%0A%28XA%29%5Et%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26amp%3Bc%5C%5C2a-b%26amp%3B2c-d%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C "XA= \left[\begin{array}{cc}1a+0b&2a-b\\c+0d&2c-d\end{array}\right] \\ \\
XA= \left[\begin{array}{cc}a&2a-b\\c&2c-d\end{array}\right] \\ \\
(XA)^t= \left[\begin{array}{cc}a&c\\2a-b&2c-d\end{array}\right] \\ \\")
Como
, os elementos correspondentes das duas matrizes são iguais.
![a=-1 \\
\\ c = 3 \\
\\ 2a-b = 2 \\
-2-b=2 \\
b=-4 \\ \\
2c-d=-6 \\
6-d=-6 \\
d=12 \\
\\
X= \left[\begin{array}{cc}-1&-4\\3&12\end{array}\right]](https://tex.z-dn.net/?f=a%3D-1+%5C%5C+%0A%5C%5C+c+%3D+3+%5C%5C+%0A%5C%5C+2a-b+%3D+2+%5C%5C%0A-2-b%3D2+%5C%5C%0Ab%3D-4+%5C%5C+%5C%5C%0A2c-d%3D-6+%5C%5C%0A6-d%3D-6+%5C%5C%0Ad%3D12+%5C%5C%0A%5C%5C%0AX%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26amp%3B-4%5C%5C3%26amp%3B12%5Cend%7Barray%7D%5Cright%5D+%0A "a=-1 \\
\\ c = 3 \\
\\ 2a-b = 2 \\
-2-b=2 \\
b=-4 \\ \\
2c-d=-6 \\
6-d=-6 \\
d=12 \\
\\
X= \left[\begin{array}{cc}-1&-4\\3&12\end{array}\right]")
Como
juniorbastos3m:
vlw! merecido os pontos!
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