4. (a) Let {u, v} be an orthonormal basis for R. Let a, b be two...

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4. (a) Let {u, v} be an orthonormal basis for R². Let a, b be two real numbers such that a² +6² = 1. Show that the vectors {w, z} given by w = au + bv z = -bu + av also form an orthonormal basis for R². (b) Define the linear subspace U = span{(1, 1, 1)} of R³. Find a basis for its orthogonal complement U (c) Find an orthogonal basis for the space U defined above. 4. (a) Let {u, v} be an orthonormal basis for R². Let a, b be two real numbers such that a² +6² = 1. Show that the vectors {w, z} given by w = au + bv z = -bu + av also form an orthonormal basis for R². (b) Define the linear subspace U = span{(1, 1, 1)} of R³. Find a basis for its orthogonal complement U (c) Find an orthogonal basis for the space U defined above.