# Subspace

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.

https://brainmass.com/math/geometry-and-topology/subspace-linear-equation-questions-128033

#### Solution Preview

Please see the attached file.

Proof:

(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 , ...

#### Solution Summary

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