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 vector...is not in the plane.
Find the vector in the plane that is the closest to v.
Please see the attached file.
(a) Since is the subspace defined by the equation , then is the set of all points that satisfy the equation. We can give a general solution. Let , then we can find two linearly independent solution and . Especially, let , we obtain the basis of . The basis is , ...
This is a set of questions regarding a subspace, vectors, and basis.