Answer
True
Work Step by Step
From the definition we know the linear system $Ax_0=b$ is obtained when $b− Ax_0$ orthogonal to every vector in colspace (A).
Therefore for every vector $b$ in $R^m$, applying the projection matrix P for the linear system $Ax = b$ to the vector $b$ results in $a$ vector that lies in colspace(A).
