Question 1

Find the Wronskian for the set of functions   .

Accepted Answer

A)  x 
B)    
C)  1 
D)    
E)  0 
A)  x 
B)    
C)  1 
D)    
E)  0

Question 2

Describe the zero vector (the additive identity) of the vector space   .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 3

The set   is linearly independent.

Accepted Answer

A) True 
 B)False

Question 4

The set   is a subspace of   with the standard operations.

Accepted Answer

A) True 
 B)False

Question 5

Find the Wronskian for the set of functions   .

Accepted Answer

A)    
B)     
C)     
D)     
E)     
A)    
B)     
C)     
D)     
E)

Question 6

the following subset of   is a subspace of   .The set of all zero functions:

Accepted Answer

A) True 
 B)False

Question 7

The set   spans   .

Accepted Answer

A) True 
 B)False

Question 8

Provided   and   , solve   for w.

Accepted Answer

A) 
  
B)   
  
C)   
  
D)  
   
E)  
   
A) 
  
B)   
  
C)   
  
D)  
   
E)

Question 9

Identify the graph of the equation   .

Accepted Answer

A)  The graph of this equation is the point   
B)  The graph of this equation is the point   
C)  The graph of this equation is an ellipse centered at   with major axis parallel to the y-axis. 
D)  The graph of this equation is the point   
E)  The graph of this equation is an ellipse centered at   with major axis parallel to the x-axis. 
A)  The graph of this equation is the point   
B)  The graph of this equation is the point   
C)  The graph of this equation is an ellipse centered at   with major axis parallel to the y-axis. 
D)  The graph of this equation is the point   
E)  The graph of this equation is an ellipse centered at   with major axis parallel to the x-axis.

Question 10

Sketch the graph of the equation   .

Accepted Answer

A)     
B)    
C)     
D)     
E)    
A)     
B)    
C)     
D)     
E)

Question 11

The set   is a basis for   .

Accepted Answer

A) True 
 B)False

Question 12

Find the transition matrix from   to   by hand.

Accepted Answer

A)    
B)    
C)    
D)     
E)     
A)    
B)    
C)    
D)     
E)

Question 13

Find the transition matrix from   to   .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 14

Provide that   , and   , write   as a linear combination of   , and   , if possible.

Accepted Answer

A)     
B)     
C)     
D)    
E)  It is not possible to write v as a linear combination of   , and   . 
A)     
B)     
C)     
D)    
E)  It is not possible to write v as a linear combination of   , and   .

Question 15

Determine whether the set,   with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

Accepted Answer

A)  This set is not a vector space. It fails the following axioms.
Commutative property
Additive identity
Distributive property 
B)  This set is not a vector space. It fails the following axioms.
Scalar identity
Associative property
Distributive property
Additive identity 
C)  This set is a vector space. All ten vector space axioms hold. 
D)  This set is not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
E)  This set is not a vector space. It fails the following axioms.
Closer under addition
Closer under scalar multiplication 
A)  This set is not a vector space. It fails the following axioms.
Commutative property
Additive identity
Distributive property 
B)  This set is not a vector space. It fails the following axioms.
Scalar identity
Associative property
Distributive property
Additive identity 
C)  This set is a vector space. All ten vector space axioms hold. 
D)  This set is not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
E)  This set is not a vector space. It fails the following axioms.
Closer under addition
Closer under scalar multiplication

Question 16

the following subset of   is a subspace of   .The set of all negative functions:

Accepted Answer

A) True 
 B)False

Question 17

Describe the zero vector (the additive identity) of the vector space   .

Accepted Answer

A)  (0, 0, 0, 0, 0) 
B)  (0, 0, 0, 0) 
C)  (0, 0, 0, 0, 0, 0) 
D)  (0, 0) 
E)  (0, 0, 0) 
A)  (0, 0, 0, 0, 0) 
B)  (0, 0, 0, 0) 
C)  (0, 0, 0, 0, 0, 0) 
D)  (0, 0) 
E)  (0, 0, 0)

Question 18

The set   spans   .

Accepted Answer

A) True 
 B)False

Question 19

W is the set of all functions that are differentiable on   . V is the set of all functions that are continuous on   . Verify W is a subspace of V.​

Accepted Answer

The answer of W is the set of all functions...

Question 20

Describe the zero vector (the additive identity) of the vector space   .

Accepted Answer

A)    
B)    
C)    
D)     
E)    
A)    
B)    
C)    
D)     
E)

Find the Wronskian for the set of functions .

Describe the zero vector (the additive identity) of the vector space .

The set is linearly independent.

The set is a subspace of with the standard operations.

Find the Wronskian for the set of functions .

the following subset of is a subspace of .The set of all zero functions:

The set spans .

Provided and , solve for w.

Identify the graph of the equation .

Sketch the graph of the equation .

The set is a basis for .

Find the transition matrix from to by hand.

Find the transition matrix from to .

Provide that , and , write as a linear combination of , and , if possible.

Determine whether the set, with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

the following subset of is a subspace of .The set of all negative functions:

Describe the zero vector (the additive identity) of the vector space .

The set spans .

W is the set of all functions that are differentiable on . V is the set of all functions that are continuous on . Verify W is a subspace of V.

Describe the zero vector (the additive identity) of the vector space .

Linear Equations

Matrices

Determinants

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Exam 4: Vector Spaces

Find the Wronskian for the set of functions .

Describe the zero vector (the additive identity) of the vector space .

The set is linearly independent.

The set is a subspace of with the standard operations.

Find the Wronskian for the set of functions .

the following subset of is a subspace of .The set of all zero functions:

The set spans .

Provided and , solve for w.

Identify the graph of the equation .

Sketch the graph of the equation .

The set is a basis for .

Find the transition matrix from to by hand.

Find the transition matrix from to .

Provide that , and , write as a linear combination of , and , if possible.

Determine whether the set, with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

the following subset of is a subspace of .The set of all negative functions:

Describe the zero vector (the additive identity) of the vector space .

The set spans .

W is the set of all functions that are differentiable on . V is the set of all functions that are continuous on . Verify W is a subspace of V.​

Describe the zero vector (the additive identity) of the vector space .

Linear Equations

Matrices

Determinants

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

W is the set of all functions that are differentiable on . V is the set of all functions that are continuous on . Verify W is a subspace of V.