Let Ax=b be a nonhomogenous system of linear equations with the unknown x ∈ |R^n. Assume that X1 ∈ |R^n and X2 ∈ |R^n are both solutions of the nonhomogenous system. Which ONE of the following statements must be true?
a) x1 + x2 is a solution of Ax = 0 b) x1 - x2 is a solution of Ax = 0 c) x1 + x2 is a solution of Ax = b d) x1 - x2 is a solution of Ax = b
I'm not really sure how to approach this question. My current approach is to make up a system of equations such that Ax = b is nonhomogenous.
So I have:
5x - 2y = 1 8x - 3y = 2
The solutions of (x,y) are (1,2) for both equations.
5(1) - 2(2) = 1 8(1) - 3(2) = 1
Not sure what to do next, if I plug in ( x , y ) for ( x1 , x2 ) in the answer choices, none of them seem to be consistent.