is it possible to have a system satifying this:

**A system of four equations in three variables such that the associated coecient matrix has no zero**

**entries, no row is a multiple of any other row, and the matrix has rank 2?**

i thought that if no row is a multiple of any other than how could u get anything other than rank 3??

I also need to somehow come up with examples of:

**A system of three equations in four variables such that the associated coeffcient matrix has no zero**

**entries, no row is a multiple of any other row, and the matrix has rank 2.**

**A system of three equations in four variables such that the associated coefficient matrix has no zero entries**

**and has rank 3.**

not sure what examples satify the above but any help would be much appreciated as this is all very new to me.

cheers