Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - True-False Review - Page 330: i

True

Since $x_p$ is a solution to the system $Ax=b$ we have $Ax_p=b$ Obtain $A(y+x_p)=Ay+Ax_p$ Since $y \in nullspace (A) \rightarrow Ay=0$ then $A(y+x_p)=b$ Hence, $y+x_p$ is also a solution the system $Ax=b$ Hence, the statement is true.