Prove the second part of Theorem 6: Let w be any solution of Ax = b, and define v_h = w - p. Show that v_h is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + V_h, with p a particular solution of Ax = b and
V_h a solution of Ax = 0.

Data from in Theorem 6

Transcribed Image Text:

Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w = p + Vh, where V₁ is any solution of the homogeneous equation Ax = 0. Vh