Week 12: Part 1: This exercise will ask you to explore the equality Null(A") = (Col(A))-. Pick a vector u in Rª and a vector v such that u and v are orthogonal; then find a vector w which cience and...

Extracted text: Week 12: Part 1: This exercise will ask you to explore the equality Null(A") = (Col(A))-. Pick a vector u in Rª and a vector v such that u and v are orthogonal; then find a vector w which cience and Technology Unleashed Interview Dec 7, 202U 1he 7 is orthogonal to both u and v. Finally, find a vector z which is orthogonal to u, v, w. For the last two steps, you should realize that you are solving a system of linear equations, and if you write them down that the system is represented by AT where the columns of A are the vectors you are trying to be orthogonal to. Now, verify with computations that the set {u, v, w, z} is linearly independent. If any of the vectors u, v, w, z are scalars of the standard basis vectors e1, e2, €3, e4 then start over. Set the matrix P = [u_v w z] and compute without calculations the vectors P-'u, P-'v, P-lw, and P-lz.