O determinante da matriz M= (1 4 0) (2 -1 1) (1 2 2) vale:?
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Oi, Greissy! Tudo bem?
Façamos pelo método de Laplace:
![M= \left[\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right] \\ \\ \\ det(M)= \left|\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right| =\\ \\ \\1.(-1)^{3+1}\left|\begin{array}{cc}4&0\\-1&1\end{array}\right| + 2.(-1)^{3+2}\left|\begin{array}{cc}1&0\\2&1\end{array}\right| + 2.(-1)^{3+3}\left|\begin{array}{cc}1&4\\2&-1\end{array}\right| \\ \\ \\ =(4.1-(-1).0)-2(1.1-2.0)+2(1.(-1)-2.4)=4-2-18 \\ \\=-16](https://tex.z-dn.net/?f=M%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B4%26amp%3B0%5C%5C2%26amp%3B-1%26amp%3B1%5C%5C1%26amp%3B2%26amp%3B2%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%5C%5C+%5C%5C+det%28M%29%3D++%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B4%26amp%3B0%5C%5C2%26amp%3B-1%26amp%3B1%5C%5C1%26amp%3B2%26amp%3B2%5Cend%7Barray%7D%5Cright%7C+%3D%5C%5C+%5C%5C+%5C%5C1.%28-1%29%5E%7B3%2B1%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D4%26amp%3B0%5C%5C-1%26amp%3B1%5Cend%7Barray%7D%5Cright%7C+%2B+2.%28-1%29%5E%7B3%2B2%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B0%5C%5C2%26amp%3B1%5Cend%7Barray%7D%5Cright%7C+%2B+2.%28-1%29%5E%7B3%2B3%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3B4%5C%5C2%26amp%3B-1%5Cend%7Barray%7D%5Cright%7C+%5C%5C+%5C%5C+%5C%5C+%3D%284.1-%28-1%29.0%29-2%281.1-2.0%29%2B2%281.%28-1%29-2.4%29%3D4-2-18+%5C%5C+%5C%5C%3D-16 "M= \left[\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right] \\ \\ \\ det(M)= \left|\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right| =\\ \\ \\1.(-1)^{3+1}\left|\begin{array}{cc}4&0\\-1&1\end{array}\right| + 2.(-1)^{3+2}\left|\begin{array}{cc}1&0\\2&1\end{array}\right| + 2.(-1)^{3+3}\left|\begin{array}{cc}1&4\\2&-1\end{array}\right| \\ \\ \\ =(4.1-(-1).0)-2(1.1-2.0)+2(1.(-1)-2.4)=4-2-18 \\ \\=-16")
Espero ter ajudado. Abraço!
Façamos pelo método de Laplace:
Espero ter ajudado. Abraço!
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