Chapter 5.3, Problem 70E

In all parts of this problem, let V be the subspace of allvectors $\stackrel{\to }{x}$ in ${ℝ}^4$ such that $x_3=x_1+x_2$ and $x_4=x_2+x_3$ .See Problems 72 and 73 of Section 4.3.
a. Find the matrix $P_V$ of the orthogonal projection ontothe subspace V in ${ℝ}^4$ . Hint: Work with one of thebases of V we considered in Problem 4.3.73.
b. What is the relationship between the subspaces Wand V defined in Exercises 69 and 70? Consequently, what is the relationship between the matrices $P_W$ and $P_V$ in Exercises 69 and 70?