Question

Let Ax=b be any consistent system of linear equations, and let x1 be a fixed solution. show that every solution to the system can be written in form x=x1+x2, where x0 is a solution to Ax=0. show that every matrix of this form is a solution.

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Answer 1

Ax = b and Ax = 0 are mostly similar and both are homogeneous

so if Ax = 0 can be expressed as x1 - x2
any solution of Ax=b can be expressed as x1 + x2

hope this helps