Let S be the the following subspace of R4: S=\operatorname{span}\left\{\left[\begin{array}{l}

1 \\

0 \\

0 \\

1

\end{array}\right],\left[\begin{array}{l}

1 \\

1 \\

1 \\

1

\end{array}\right]\right\} ) Give dim(S) and dim(S¹). S is the orthogonal complement of S. (b) Compute Ps and Ps, the projection matrices on S and S, respectively. (c) What are the relationships between the column spaces and nullspaces of Ps and Psi.e., C(Ps), N(Ps), C(PS¹), and N (PS¹). (d) Give orthonormal bases for each of C(Ps), N(Ps), C(Ps+), and N(PS1). (e) Give the eigenvalues of Ps, along with their algebraic and geometric multiplicities.