Question

8. a. If A is 5 x 5 matrix and det(A) = 3 then det(2A) = --------- b. If A is 100 x 100 matrix and det( A) = m then det(-A) = -----

Answer 1

Answer:

a) det(A)=96; b) det(A)=m;

Step-by-step explanation:

If we have a $n \times n$ matrix A and a constant $t \in \mathbb{R}$. It holds that $\det(tA)=t^n\det(A)$, hence

(a) If A is a $5x5$ matrix and $\det(A)=3$, then we have

$\det(2A)=2^5\cdot \det(A)= 32 \cdot 3=96$

(b) If A is $100 \times 100$ matrix and $\det(A)=m$, then we have

$\det(-A)=(-1)^{100}\det(A)=(-1)^{100}\cdot m=1 \cdot m = m$