Question 1

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

Accepted Answer

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

Question 2

Find a basis for the subspace of   spanned by   .

Accepted Answer

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

Question 3

Determine whether   is a basis for   . If it is, write   as a linear combination of the vectors in S.?

Accepted Answer

A)  S is a basis for   and   
B)  S is a basis for   and ?   
C)  S is a basis for   and   
D)  S is a basis for   and   
E)  S is not a basis for   
A)  S is a basis for   and   
B)  S is a basis for   and ?   
C)  S is a basis for   and   
D)  S is a basis for   and   
E)  S is not a basis for   E

Question 4

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

Accepted Answer

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

Question 5

Find the coordinate matrix of   relative to the standard basis in   .

Accepted Answer

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

Question 6

? The set   is a subspace of   with the standard operations.

Accepted Answer

A) True 
 B)False

Question 7

Find the coordinate matrix of   in   relative to the basis   .

Accepted Answer

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

Question 8

Find a basis for the row space of a matrix   .

Accepted Answer

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

Question 9

Find a basis for and the dimension of the solution space of   .

Accepted Answer

A)    , dim = 1 
B)    , dim = 3 
C)     , dim = 1 
D)    ? , dim = 2 
E)     , dim = 3 
A)    , dim = 1 
B)    , dim = 3 
C)     , dim = 1 
D)    ? , dim = 2 
E)     , dim = 3

Question 10

Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic defined by the function below.

Accepted Answer

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

Question 11

Provided   and   , find w such that   .

Accepted Answer

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

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

Given that   , the coordinate matrix of x relative to a (nonstandard) basis   find the coordinate vector of x relative to the standard basis in   .

Accepted Answer

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

Question 14

Determine whether the set of all third-degree polynomial functions as given below, whose graphs pass through the origin 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 not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
D)  This set is a vector space. All ten vector space axioms hold. 
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 not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
D)  This set is a vector space. All ten vector space axioms hold. 
E)  This set is not a vector space. It fails the following axioms.
Closer under addition
Closer under scalar multiplication

Question 15

The set   spans   .

Accepted Answer

A) True 
 B)False

Question 16

Determine whether   is a basis for   . If it is, write   as a linear combination of the vectors in S.?

Accepted Answer

A)  S is a basis for   and   
B)  S is a basis for   and   
C)  S is a basis for   and   
D)  S is a basis for   and   
E)  S is not a basis for   
A)  S is a basis for   and   
B)  S is a basis for   and   
C)  S is a basis for   and   
D)  S is a basis for   and   
E)  S is not a basis for

Question 17

Determine whether the set of all first-degree polynomial functions as given below, whose graphs pass through the origin 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 not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
D)  This set is a vector space. All ten vector space axioms hold. 
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 not a vector space. It fails the following axioms.
Additive identity
Additive inverse
Associative property
Scalar identity 
D)  This set is a vector space. All ten vector space axioms hold. 
E)  This set is not a vector space. It fails the following axioms.
Closer under addition
Closer under scalar multiplication

Question 18

Write the standard basis for the vector space   .

Accepted Answer

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

Question 19

The set of all   singular matrices is a subspace of   .

Accepted Answer

A) True 
 B)False

Question 20

Given that   , the coordinate matrix of x relative to a (nonstandard) basis   . Find the coordinate vector of x relative to the standard basis in   .

Accepted Answer

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

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

Find a basis for the subspace of spanned by .

Determine whether is a basis for . If it is, write as a linear combination of the vectors in S.?

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

Find the coordinate matrix of relative to the standard basis in .

? The set is a subspace of with the standard operations.

Find the coordinate matrix of in relative to the basis .

Find a basis for the row space of a matrix .

Find a basis for and the dimension of the solution space of .

Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic defined by the function below.

Provided and , find w such that .

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

Given that , the coordinate matrix of x relative to a (nonstandard) basis find the coordinate vector of x relative to the standard basis in .

Determine whether the set of all third-degree polynomial functions as given below, whose graphs pass through the origin with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

The set spans .

Determine whether is a basis for . If it is, write as a linear combination of the vectors in S.?

Determine whether the set of all first-degree polynomial functions as given below, whose graphs pass through the origin with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

Write the standard basis for the vector space .

The set of all singular matrices is a subspace of .

Given that , the coordinate matrix of x relative to a (nonstandard) basis . Find the coordinate vector of x relative to the standard basis in .

Linear Equations

Matrices

Determinants

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Exam 4: Vector Spaces

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

Find a basis for the subspace of spanned by .

Determine whether is a basis for . If it is, write as a linear combination of the vectors in S.?

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

Find the coordinate matrix of relative to the standard basis in .

? The set is a subspace of with the standard operations.

Find the coordinate matrix of in relative to the basis .

Find a basis for the row space of a matrix .

Find a basis for and the dimension of the solution space of .

Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic defined by the function below.

Provided and , find w such that .

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

Given that , the coordinate matrix of x relative to a (nonstandard) basis find the coordinate vector of x relative to the standard basis in .

Determine whether the set of all third-degree polynomial functions as given below, whose graphs pass through the origin with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

The set spans .

Determine whether is a basis for . If it is, write as a linear combination of the vectors in S.?

Determine whether the set of all first-degree polynomial functions as given below, whose graphs pass through the origin with the standard operations, is a vector space. If it is not, then determine the set of axioms that it fails.

Write the standard basis for the vector space .

The set of all singular matrices is a subspace of .

Given that , the coordinate matrix of x relative to a (nonstandard) basis . Find the coordinate vector of x relative to the standard basis in .

Linear Equations

Matrices

Determinants

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters