Is the Solution Set of Ax=b a Subspace of R^n?

[aan]

Please anyone solve this question or can even email me on my ID abu_95bakar@yahoo.com...

For the following question determine whether the set S is a sub space of the given vectorspace V.

v=Rn( where n represent dimension), S is the solution set of the sysytem Ax=b, where A is an mxn matrix.



PLEASE HELP! THANX A MILLION IN ADVANCE.

 

[HallsofIvy]

Please anyone solve this question or can even email me on my ID abu_95bakar@yahoo.com...

For the following question determine whether the set S is a sub space of the given vectorspace V.

v=Rn( where n represent dimension), S is the solution set of the sysytem Ax=b, where A is an mxn matrix.



PLEASE HELP! THANX A MILLION IN ADVANCE.

Looks straight forward to me. To prove something is a subspace, show that it satisifies the properties of a subspace: specifically that it is closed under addition and scalar multiplication. If x and y are in this set then Ax= b and Ay= b so A(x+y)= Ax+ Ay= b+ b= 2b. What does that tell you?