Question 32995
 consistent system Ax=b (m linear equations, n unknowns)
 form a subspace of Rn?

 Note b is in R^m, A an n x m  matrix

 Let V = { x in R^n| Ax = b }
 Since any vector space must contain the zero vector, b must be 0.

 Clearly if x,y in V and scalrs a,b , we have
 A(ax+by) =  a Ax + b Ay = 0.
 Hence, V = { x in R^n| Ax = 0 } is a subspace of R^n.

 This proves b = 0 is the sufficient (& necessary) condition for the solution
 set V to be a subspace of R^n.

 Kenny