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Dadas as matrizes A= -1 3 e B= 2 -1 determinem:
2 -8 3 0
a) Det A
b) Det B
c) Det (A+B)
d) Det A + det B


RESOLVENDO

\( det~\left[\begin{array}{cc}a& b\\c& d\end{array}\right]=\left|\begin{array}{cc}a& b\\c& d\end{array}\right|=ad-bc \)
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a)
\( det~\left[\begin{array}{cc}-1&3\\2&-8\end{array}\right]=(-1)(-8)-3\cdot2\\det~\left[\begin{array}{cc}-1&3\\2&-8\end{array}\right]=8-6\\boxed{\boxed{det~\left[\begin{array}{cc}-1&3\\2&-8\end{array}\right]=2}} \)
b)
\( det~\left[\begin{array}{cc}2&-1\\3&0\end{array}\right]=2\cdot0-(-1)\cdot3\\det~\left[\begin{array}{cc}2&-1\\3&0\end{array}\right]=0+3\\boxed{\boxed{det~\left[\begin{array}{cc}2&-1\\3&0\end{array}\right]=3}} \)
c)
Primeiro, vamos achar A + B:
\( A+B=\left[\begin{array}{cc}-1&3\\2&-8\end{array}\right]+\left[\begin{array}{cc}2&-1\\3&0\end{array}\right]\\A+B=\left[\begin{array}{cc}(-1+2)&(3-1)\\(2+3)&(-8+0)\end{array}\right]\\A+B=\left[\begin{array}{cc}1&2\\5&-8\end{array}\right] \)
Achando o determinante dessa matriz:
\( det~\left[\begin{array}{cc}1&2\\5&-8\end{array}\right]=1(-8)-2\cdot5\\det~\left[\begin{array}{cc}1&2\\5&-8\end{array}\right]=-8-10\\boxed{\boxed{det~\left[\begin{array}{cc}1&2\\5&-8\end{array}\right]=-18}} \)
d)
\( det~A+det~B=2+3\\boxed{\boxed{det~A+det~B=5}} \)



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