Question

Se det A =  $\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$ = 10 calcule:

**  det B = $\left[\begin{array}{ccc}b&a\\d&c\\\end{array}\right]$ 

Answer 1

Calculemos o determinante da matriz A:

$a\cdot d-b\cdot c=10\\ad-bc=10$

 Calculemos det B,

$\text{det b}=b\cdot c-a\cdot d\\\text{det b}=bc-ad\\\text{det b}=-1(-bc+ad)\\\text{det b}=-(ad-bc)\\\text{det b}=-(+10)\\\boxed{\boxed{\text{det b}=-10}}$