por favor me ajudem achar o determinante desta matriz de ordem 4![\left[\begin{array}{cccc}5&3&1&0\\2&0&-1&0\\1&-1&-2&0\\2&3&-3&1\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%26amp%3B3%26amp%3B1%26amp%3B0%5C%5C2%26amp%3B0%26amp%3B-1%26amp%3B0%5C%5C1%26amp%3B-1%26amp%3B-2%26amp%3B0%5C%5C2%26amp%3B3%26amp%3B-3%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{cccc}5&3&1&0\\2&0&-1&0\\1&-1&-2&0\\2&3&-3&1\end{array}\right]")
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Olá Ellen,
dada a matriz de ordem 4, só vamos calcular o determinante A44, pois os demais são colunas nulas, as quais escolhemos para trabalhar. Aplicando o teorema de Laplace, teremos:
![D= \left|\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\\a_{41}&a_{42}&a_{43}&a_{44}\end{array}\right| D_t=\left| \begin{array}{cccc}5&~~3&~~1&~~0\\2&~~0&-1&~~0\\1&-1&-2&~~0\\2&~~3&-3&~~\boxed{1}\end{array}\right|\\\\\\
D_t=\boxed{1}*cof*D_t\\\\
D_t=1*(-1)^{4+4} \left|\begin{array}{ccc}5&3&~~1\\2&0&-1\\1&-1&-2\end{array}\right| \left\begin{array}{ccc}5&~~3\\2&~~0\\1&-1\end{array}\right\\\\
D_t=(-1)^8*[0-3-2-0-5+12]\\
D_t=1*2\\\\
\boxed{D_t=2}](https://tex.z-dn.net/?f=++D%3D++%5Cleft%7C%5Cbegin%7Barray%7D%7Bcccc%7Da_%7B11%7D%26amp%3Ba_%7B12%7D%26amp%3Ba_%7B13%7D%26amp%3Ba_%7B14%7D%5C%5Ca_%7B21%7D%26amp%3Ba_%7B22%7D%26amp%3Ba_%7B23%7D%26amp%3Ba_%7B24%7D%5C%5Ca_%7B31%7D%26amp%3Ba_%7B32%7D%26amp%3Ba_%7B33%7D%26amp%3Ba_%7B34%7D%5C%5Ca_%7B41%7D%26amp%3Ba_%7B42%7D%26amp%3Ba_%7B43%7D%26amp%3Ba_%7B44%7D%5Cend%7Barray%7D%5Cright%7C+D_t%3D%5Cleft%7C++%5Cbegin%7Barray%7D%7Bcccc%7D5%26amp%3B%7E%7E3%26amp%3B%7E%7E1%26amp%3B%7E%7E0%5C%5C2%26amp%3B%7E%7E0%26amp%3B-1%26amp%3B%7E%7E0%5C%5C1%26amp%3B-1%26amp%3B-2%26amp%3B%7E%7E0%5C%5C2%26amp%3B%7E%7E3%26amp%3B-3%26amp%3B%7E%7E%5Cboxed%7B1%7D%5Cend%7Barray%7D%5Cright%7C%5C%5C%5C%5C%5C%5C%0AD_t%3D%5Cboxed%7B1%7D%2Acof%2AD_t%5C%5C%5C%5C%0AD_t%3D1%2A%28-1%29%5E%7B4%2B4%7D++%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D5%26amp%3B3%26amp%3B%7E%7E1%5C%5C2%26amp%3B0%26amp%3B-1%5C%5C1%26amp%3B-1%26amp%3B-2%5Cend%7Barray%7D%5Cright%7C++%5Cleft%5Cbegin%7Barray%7D%7Bccc%7D5%26amp%3B%7E%7E3%5C%5C2%26amp%3B%7E%7E0%5C%5C1%26amp%3B-1%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%0AD_t%3D%28-1%29%5E8%2A%5B0-3-2-0-5%2B12%5D%5C%5C%0AD_t%3D1%2A2%5C%5C%5C%5C%0A%5Cboxed%7BD_t%3D2%7D+ "D= \left|\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\\a_{41}&a_{42}&a_{43}&a_{44}\end{array}\right| D_t=\left| \begin{array}{cccc}5&~~3&~~1&~~0\\2&~~0&-1&~~0\\1&-1&-2&~~0\\2&~~3&-3&~~\boxed{1}\end{array}\right|\\\\\\
D_t=\boxed{1}*cof*D_t\\\\
D_t=1*(-1)^{4+4} \left|\begin{array}{ccc}5&3&~~1\\2&0&-1\\1&-1&-2\end{array}\right| \left\begin{array}{ccc}5&~~3\\2&~~0\\1&-1\end{array}\right\\\\
D_t=(-1)^8*[0-3-2-0-5+12]\\
D_t=1*2\\\\
\boxed{D_t=2}")
Tenha ótimos estudos =))
dada a matriz de ordem 4, só vamos calcular o determinante A44, pois os demais são colunas nulas, as quais escolhemos para trabalhar. Aplicando o teorema de Laplace, teremos:
Tenha ótimos estudos =))
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