Let V be a5 × 3 matrix whose columns are orthonormal vectors v1, v2, v3 in 5 (b) Write a singular value decomposition for PV that includes the vectors v1, v2, v3. What are the singular values of PV ? (c) Show that PVPV =PV (d) Show that the range of the matrix I − PV is the null space of PV and, moreover, (I − PV ) (I − PV ) = I − PV . The matrix PV is the orthogonal projector to V , and I − PV is the ⊥ R . Show that