Question 1

If   and   are subspaces of a vector space V and   , then   .

Accepted Answer

A) True 
 B)False

Question 2

In the vector space V of all differentiable functions   , let S be the set of all functions f such that   . Determine if S is a subspace of V, and if not explain why.

Accepted Answer

S is not a subspace,

Question 3

If S is a subspace of the polynomial space   , then   for some m with   .

Accepted Answer

A) True 
 B)False

Question 4

Determine if the set of vectors   is linearly independent in P.

Accepted Answer

The set is

Question 5

In the vector space   , let S be the set of matrices A such that   . Determine if S is a subspace of   , and if not explain why.

Accepted Answer

S is not a subspace,

If and are subspaces of a vector space V and , then .

In the vector space V of all differentiable functions , let S be the set of all functions f such that . Determine if S is a subspace of V, and if not explain why.

If S is a subspace of the polynomial space , then for some m with .

Determine if the set of vectors is linearly independent in P.

In the vector space , let S be the set of matrices A such that . Determine if S is a subspace of , and if not explain why.

Systems of Linear Equations

Euclidean Space

Matrices

Subspaces

Determinants

Eigenvalues and Eigenvectors

Orthogonality

Linear Transformations

Inner Product Spaces

Additional Topics and Applications

Filters

Exam 7: Vector Spaces