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.

Vector Space and Subspace. Define vectors pace and subspace with examples. ... ii) A necessary and sufficient condition for a subset of vectors to be a subspace. ...

Prove that U is a Subspace of V and is Contained in W. Please view the attached file for the full solution. ... Then W is a subspace of V. Let U = {( a_1, a_2, ... ...

Prove that the Kernel of a homomorphism is a subspace. Prove that the Kernel of a homomorphism is a subspace. ... We have to prove that Ker is a subspace of . ...

Suppose that is a Banach space over K. A subspace M of is said to be complemented in if there exists a subspace N of such that =MN, that is if , then there ...

... 2. i) It is not a subspace, since the zero polynomial does not belong it. ... To find its basis, let us note that it is isomorphic to the following subspace of : . ...

Vector Subspace of the Vector Space. ... I understand how to verify a vector subspace of a vector space, if it is closed under addition and scaler multiplication. ...

Finding Basis and Dimension of the Subspace generated by given vectors. ... Dimension of Subspace of M2(R) generated by the given matrix = 2 and the basis is .... ...