What I did:The linear system in x,y:

has a unique solution precisely when:

a).

b).

c).

d).

The determinant of the matrix cannot be zero so:

Hence the answer is d).

I have a nagging feling about that though....

I know that for a transformation to be linear:Let be given by:

which of and is a linear transformation?

a).

b).

c).

d). none of them

applying these, is the only linear transformation so the answer is b).

Can someone check these answers?