Answer:
It is proved that is a solution of Ax=b.
Step-by-step explanation:
As given let w and p be a solution of Ax=b. Then,
and
Defining,
To show is a solution of Ax=b, we have to show . Then,
(By putting value of )
(By distributive law)
(Since w and p are solution of Ax=b)
Hence become a solution of the homogenous system Ax=b.
Since w and p are solution of Ax=b, and any linear combination of the solutions again a solution of Ax=b, this shows that every solution of Ax=b is of the form where is a solution of Ax=0.