Question

Demuestre que det (4•B) = 16 • det (A)
Ayúdenme por fa​

Answer 1

Hola !

Sea la matriz,

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

Tienes que,

$det(a) = ad-bc$

Sea ahora,

$4A = 4\cdot \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = \left[\begin{array}{ccc}4a&4b\\4c&4d\end{array}\right]$

El determinante es,

$det(4A) = 4^2ad-4^2bc = 4^2 (ad-bc ) = 16(ad-bc) = 16\cdot det(A)$

Saludos ! :)