Question

O valor do determinante. 2 3 1
1 1 -1
5 7 -3 é?

Answer 1

$\left[\begin{array}{ccc}2&3&1\\1&1&-1\\5&7&-3\end{array}\right]$

$\left[\begin{array}{ccc}2&3&1\\1&1&-1\\5&7&-3\end{array}\right] \left[\begin{array}{ccc}2&3\\1&1\\5&7\end{array}\right]$

Det = {2 . 1 . (-3) + 3 . (-1) . 5 + 1 . 1 . 7} - {1 . 1 . 5 + 2 . (-1) . 7 + 3 . 1 . (-3)}

= {-6 + (-15) + 7} - {5 + (-14) + (-9)}

= (-14) - (-18)

= 4