1. By first finding the projection onto $V^{\perp}$, find the projection of the given vector $\mathbf{b} \in \mathbb{R}^m$
onto the given hyperplane $V \subset \mathbb{R}^m$.
a. $V = \{x_1 + x_2 + x_3 = 0\} \subset \mathbb{R}^3$, $\mathbf{b} = (2, 1, 1)$
*b. $V = \{x_1 + x_2 + x_3 = 0\} \subset \mathbb{R}^4$, $\mathbf{b} = (0, 1, 2, 3)$
c. $V = \{x_1 - x_2 + x_3 + 2x_4 = 0\} \subset \mathbb{R}^4$, $\mathbf{b} = (1, 1, 1, 1)$