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Linear Equation Questions. See attached file for full problem description.

Let S be the subspace....
Explain why this linear equation represents a subspace and find a basis for it.
Clearly explain why this subspace is a plane.
Find two orthogonal vectors in the plane.
Make the set you found orthonormal.
Explain why your set is a basis for the plane.
Show that the not in the plane.
Find the vector in the plane that is the closest to v.


Solution Summary

This is a set of questions regarding a subspace, vectors, and basis.