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Endterm Exam

Variant-1

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Show that given set is a basis for .

3. (25 points) Given the basis , find the coordinates of x:

4. (25 points) Determine whether the given set is a vector space.

Endterm Exam

Variant-2

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

a) Basis for Col A

b) Basis for Nul A

c) Rank and dimNul A

2. (25 points) Show that given set is a basis for .

3. (25 points) Given the basis , , find the coordinates of x:

4. (25 points) Determine whether the given set is a vector space.

Endterm Exam

Variant-3

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors form a basis for .

3. (25 points) Given the basis , , find the coordinates of x:

4. (25 points) Determine whether the given set is a vector space.

Endterm Exam

Variant-4

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors form a basis for .

3. (25 points) Given the basis , , find the coordinates of x:

4. (25 points) Determine whether the given set is a vector space.

Endterm Exam

Variant-5

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors form a basis for .

4. (25 points) Determine whether the given set is a vector space.

Endterm Exam

Variant-6

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors is a subspace for

3. (25 points) Answer to the following questions.

1. If A is a 6 8 matrix, what is the largest possible dimension of rank A? 


2. If you are given with the change of the coordinates matrtix from basis B to the basis C. How to find the change of the coordinates matrtix from C to B?

4. (25 points) Let F = {f₁, f₂, f₃} and D = {d₁, d₂, d₃} be bases for a vector space V, and suppose

, , and .

1. Find the change-of-coordinates matrix from F to D

2. Find for

Endterm Exam

Variant-7

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

a)Basis for Col A

b) Basis for Nul A

c)Rank and dimNul A

2. (25 points) Determine whether the given set of vectors is a subspace for

3. (25 points) Answer to the following questions.

1. If A is a 7 5 matrix, what is the largest possible dimension of rank A? 


2. What is definition of the basis for some subspace?

4. (25 points) Let F = {f₁, f₂, f₃} and D = {d₁, d₂, d₃} be bases for a vector space V, and suppose

, , and .

1. Find the change-of-coordinates matrix from F to D

2. Find for

Endterm Exam

Variant-8

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors is a subspace for

3. (25 points) Answer to the following questions.

1. If A is a 6 8 matrix with 4 pivots, what is a dimension of the null space of A? 


2. Is it possible to the change of coordinates matrix if given to bases with different dimension?

4. (25 points) Let F = {f₁, f₂, f₃} and D = {d₁, d₂, d₃} be bases for a vector space V, and suppose

, , and .

1. Find the change-of-coordinates matrix from F to D

2. Find for

Endterm Exam

Variant-9

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors is a subspace for

3. (25 points) Answer to the following questions.

1. If A is a 5 4 matrix, what is the smallest possible dimension of Nul A? 


2. Consider the basis , , and the given vector x. How to find the coordinates of vector x?

4. (25 points) Let F = {f₁, f₂, f₃} and D = {d₁, d₂, d₃} be bases for a vector space V, and suppose

, , and .

1. Find the change-of-coordinates matrix from F to D

2. Find for

Endterm Exam

Variant-10

Group ____________ Name_______________________________

1. (25 points) Find the following things for the given system:

1. Basis for Col A

2. Basis for Nul A

3. Rank and dimNul A

2. (25 points) Determine whether the given set of vectors is a subspace for