Homogeneous linear system

1. Aug 2, 2008

golriz

I have a question:
If the vectors of v & u are solutions of the nonhomogeneous linear system Ax=b, then ru+sv is a solution of the nonhomogeneous system for any real values of r and s.
is this statement true?
is this statement true for homogeneous systems too?

2. Aug 2, 2008

konthelion

Hint: When a nonhomogeneous linear system has infinite solutions, then the general solutions can be written in parametric vector form.

This can be used to answer both questions.

3. Aug 2, 2008

Defennder

You should be able to find a counterexample easily for the first question. For the second, try writing the matrix equation for Ax=b using ru+sv.