Erplore the equality Null(A) (Col(A). Pick a vector u in R' and a vector v such...

  

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Erplore the equality Null(A") (Col(A). Pick a vector u in R' and a vector v such that u and v are orthogonal; then find a vector uw which 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 A" 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 2] and compute without calculations the vectors P-lu, P-'v, P-'w, and P-s. %3D Erplore the equality Null(A") (Col(A). Pick a vector u in R' and a vector v such that u and v are orthogonal; then find a vector uw which 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 A" 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 2] and compute without calculations the vectors P-lu, P-'v, P-'w, and P-s. %3D

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