Question

Sejam as matrizes nxn com detA = 3 e detB = -2. Ache os determinantes indicados:

d) det(3BT) e)det(A.AT)

Answer 1

Explicação passo-a-passo:

d)

$\sf det~(3B^t)=det~(3B)$

$\sf det~(3B^t)=3^n\cdot det~B$

$\sf det~(3B^t)=\red{3^n\cdot(-2)}$

e)

$\sf det~(A\cdot A^t)=det~(A)\cdot det~(A^t)$

$\sf det~(A\cdot A^t)=det~(A)\cdot det~(A)$

$\sf det~(A\cdot A^t)=3\cdot3$

$\sf det~(A\cdot A^t)=\red{9}$