Can someone check my answer! Thank you!

[LaraCroft]

1. The problem statement, all variables and given/known data
If a 4x4 matrix A with rows v1, v2, v3 and v4 has determinant detA =-2

then

then det (v1, 9v2+5v3, 5v2+8v3, v4) =___?


2. Relevant equations



3. The attempt at a solution

Ok, so I think it should be -18 (since 9 x -2). I mean the determinant should not change when adding columns to each other, however multiplying should have an effect, but I am not quite sure what happened to the v3, like do I multiply the determinant by 8, or 5, or none?

[Dick]

I'll give you a sample, det(v1,9*v2+5*v3,v3,v4)=
det(v1,9*v2,v3,v4)+det(v1,5*v3,v2,v5)=
9*det(v1,v2,v3,v4)+5*det(v1,v3,v3,v4). What's that? Now what happens if you put the linear combination in for v3 as well?