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

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SUMMARY

The discussion centers on determining whether the solution set S of the equation Ax = b is a subspace of the vector space R^n, where A is an m x n matrix. To establish that S is a subspace, it is essential to demonstrate that S is closed under addition and scalar multiplication. The argument presented indicates that if x and y are in S, then A(x+y) = Ax + Ay = b + b, which suggests that S does not satisfy the subspace criteria since the result is not necessarily equal to b.

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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.
 
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aan said:
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?
 

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