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

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

Explanation:

If we have a
`n * 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 * 100` matrix and
`\det(A)=m`, then we have

`\det(-A)=(-1)^(100)\det(A)=(-1)^(100)\cdot m=1 \cdot m = m`