Question

por favor me ajudem achar o determinante desta matriz de ordem 4$\left[\begin{array}{cccc}5&3&1&0\\2&0&-1&0\\1&-1&-2&0\\2&3&-3&1\end{array}\right]$

Answer 1

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:

$D= \left|\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\\a_{41}&a_{42}&a_{43}&a_{44}\end{array}\right| D_t=\left| \begin{array}{cccc}5&~~3&~~1&~~0\\2&~~0&-1&~~0\\1&-1&-2&~~0\\2&~~3&-3&~~\boxed{1}\end{array}\right|\\\\\\ D_t=\boxed{1}*cof*D_t\\\\ D_t=1*(-1)^{4+4} \left|\begin{array}{ccc}5&3&~~1\\2&0&-1\\1&-1&-2\end{array}\right| \left\begin{array}{ccc}5&~~3\\2&~~0\\1&-1\end{array}\right\\\\ D_t=(-1)^8*[0-3-2-0-5+12]\\ D_t=1*2\\\\ \boxed{D_t=2}$

Tenha ótimos estudos =))