Hallar la determinante de $$ A = \begin{pmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{pmatrix} $$
$$ A = \begin{pmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{pmatrix} $$ Entonces $$ |A| = \begin{vmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{vmatrix} $$
$$ = 1 \begin{vmatrix} 5 & 6\\ 8 & 9 \end{vmatrix} - 2 \begin{vmatrix} 4 & 6\\ 7 & 9 \end{vmatrix} + 3 \begin{vmatrix} 4 & 5\\ 7 & 8 \end{vmatrix} $$
$$ = 1(-3) -2(-6)+3(-3) = -3+12-9 =0 $$