Question

calcule o determinante da matriz da ordem 3×3 pela regra de sarrus e pelo teorema de laplace

Answer 1

O determinante pela Regra de Sarrus:

$B= \left|\begin{array}{ccc}1&2&1\\2&-1&-2\\3&0&-1\end{array}\right| \left\begin{array}{ccc}1&2\\2&-1\\3&0\end{array}\right \\ \\ \\ \to-3*(-1)*1=3 \\ \to0*(-2)*1=0 \\ \to-(-1)*2*2=4 \\ \\ \\ \\\to1*2*0 =0 \\ \to2-(2)*3=-12 \\ \to1*(-1)*(-1)=1\\\\DetB=3+0+4+0-12+1\\\boxed{\boxed{DetB=-4}}$




O determinante pelo Teorema de Laplace:

$B= \left|\begin{array}{ccc}1&2&1\\2&-1&-2\\3&0&-1\end{array}\right| \\ \\ \\ 2*(-1)^{1+2}* \left|\begin{array}{ccc}2&-2\\3&-1\\\end{array}\right| +(-1)*(-1)^{2+2}*\left|\begin{array}{ccc}1&1\\3&-1\\\end{array}\right|= \\ \\ -2* [\ 2*(-1)-3*(2)]-1*[\ 1*(-1)-3*1]= \\ \\ -2[\ -2+6]-1*[-1-3]= \\ \\ -2*[4]-1*[-4]=-8+4=\\\\\boxed{\boxed{-4}}$