Please show all steps and operations clearly please Show tha

Please show all steps and operations clearly please.

Show that the set of all solutions to the inhomogenous system Az y, y 0 is not a subspace.

To observe this, suppose that x1 and x2 are two solutions.

We have a subspace if any linear combination of these two vectors is again a solution.

So we compute

A(c1x1 + c2x2) = c1Ax1 + c2Ax2

= c1y + c2y.

= (c1 + c2)y,

Since for general c1, c2 the right hand side is not equal to y, this is not a subspace

hence proved