Question

calcule o valor determinante da matriz A=4; 5; 2; 1 ;7 ;1; 0; 6; 3

Answer 1

Após resolver os cálculos, concluímos que o determinante da matriz é igual a 57.

Utilizando o Teorema de Laplace:

$\sf A=\left[ \begin{array}{ccc}\sf 4&\sf5&\sf2\\\sf1&\sf7&\sf1\\\sf0&\sf6&\sf3\end{array} \right]$

$\displaystyle{ \mathsf{ D=\sum a_{ij}\cdot A_{ij}}}$

$\mathsf{D=a_{11}\cdot A_{11}+ a_{12}\cdot A_{12}+a_{13}\cdot A_{13}}$

$\mathsf{D=4\cdot A_{11}+ 5\cdot A_{12}+ 2\cdot A_{13} }$

$\mathsf{A_{11}=(-1)^{1+1}\cdot\left[\begin{array}{cc} \sf7&\sf1\\\sf6&\sf3\end{array}\right]=1\cdot15=15 }$

$\mathsf{A_{12}=(-1)^{1+2}\cdot\left[\begin{array}{cc}\sf 1&\sf1\\\sf 0&\sf3\end{array}\right]= -1\cdot3=-3 }$

$\mathsf{A_{13}= (-1)^{1+3}\cdot \left[\begin{array}{cc}\sf1&\sf7\\\sf0&\sf6\end{array}\right]=1\cdot6=6 }$

$\mathsf{D=4\cdot15+5\cdot(-3)+ 2\cdot6}$

$\mathsf{ D=60-15+12}$

$\boxed{\boxed{\mathsf{D=57}} }$

Portanto, o valor do determinante é igual a 57.

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