Determinant of 4x4 Matrix with Given Value and Variable Columns

[LaraCroft]

Homework Statement

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) =___?

Homework Equations

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?