Question

Folosind proprietatile determinantului sa se calculeze
| 0 a b |. | 1 1 1 |
| -a 0 c | , | a b c |
| -b -c 0 | | b+c c+a a+b |

Answer 1

Explicație pas cu pas:

$\left|\begin{array}{ccc}0&a&b\\-a&0&c\\-b&-c&0\end{array}\right| =$

$= 0 \cdot \left|\begin{array}{ccc}0&c\\-c&0\end{array}\right| - a \cdot \left|\begin{array}{ccc}-a&c\\-b&0\end{array}\right|+ b \cdot \left|\begin{array}{ccc}-a&0\\-b&-c\end{array}\right|$

$= - a \cdot (0 + bc) + b \cdot (ac - 0)$

$= -abc + abc = \bf 0$