Multiple Choice Assignment For Linear Algebra

Chapter 1 Make up Exam

Name___________________________________ Date: _______________

 

This make up is due Monday 22/09/2014. This make up exam worth %50

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Q 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
 

 

 

 

                                       

 

 

MULTIPLE CHOICES

Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) The columns of  =  are  =  ,  =  ,  =  .

 

Suppose that T is a linear transformation from  into  such that

 

T( ) =  , T( ) =  , and T( ) = .

 

Find a formula for the image of an arbitrary x =  in .

 

A)

T =           B)

T = 

C)

T =                D)

T = 

 

2) Let T:  ->  be a linear transformation that maps u =  into  and maps v =  into  .

Use the fact that T is linear to find the image of 

A)

     B)

     C)

   D)

 

3) Find the general solution of the homogeneous system below. Give your answer as a vector.

 + 2 – 3 = 0

4 + 7 – 9 = 0

 – 3 + 6 = 0

 

A)

 =           B)

 = 

C)

 =                       D)

 = 

 

4) Describe all solutions of Ax = b, where

A =  and b = .

 

Describe the general solution in parametric vector form.

A)

 =  +                        B)

 =  + 

C)

 =  +                       D)

 =  + 

 

5) For what values of h are the given vectors linearly independent?

 

A) Vectors are linearly independent for h ≠ -4

B) Vectors are linearly independent for h = -4

C) Vectors are linearly dependent for all h

D) Vectors are linearly independent for all h

 

6) Let = , =  .

 

Determine if the set {} is linearly independent.

 

A) No    B) Yes

 

7) For what values of h are the given vectors linearly independent?

 

A) Vectors are linearly independent for h = -4

B) Vectors are linearly dependent for all h

C) Vectors are linearly independent for all h

D) Vectors are linearly independent for h ≠ -4

 

8) Let A =  and u = .

Define a transformation T:  ->  by T(x) = Ax. Find T(u), the image of u under the transformation T.

 

A)

      B)

     C)

      D)

 

9) Let A =  and b = .

Define a transformation T:  ->  by T(x) = Ax.

If possible, find a vector x whose image under T is b. Otherwise, state that b is not in the range of the transformation T.

 

A)

B)

C)

b is not in the range of the transformation T.

D)

 

Describe geometrically the effect of the transformation T.

10) Let A = .

Define a transformation T by T(x) = Ax.

 

A) Projection onto the -axis       B) Vertical shear

C) Horizontal shear          D) Projection onto the -plane

 

Solve the problem.

11) The columns of  =  are  =  ,  =  ,  =  .

 

Suppose that T is a linear transformation from  into  such that

 

T( ) =  , T( ) =  , and T( ) = .

 

Find a formula for the image of an arbitrary x =  in .

 

A)

T =               B)

T = 

C)

T =           D)

T = 

 

Find the standard matrix of the linear transformation T.

12) T:  ->  rotates points (about the origin) through  π radians (with counterclockwise rotation for a positive angle).

 

A)

              B)

   C)

   D)

 

13) T:  ->  first performs a vertical shear that maps  into  + 4, but leaves the vector  unchanged, then reflects the result through the horizontal -axis.

A)

 B)

             C)

              D)

 

Determine whether the linear transformation T is one-to-one and whether it maps as specified.

14) Let T be the linear transformation whose standard matrix is

A = .

Determine whether the linear transformation T is one-to-one and whether it maps  onto .

 

A) One-to-one; not onto             B) Not one-to-one; not onto 

C) Not one-to-one; onto              D) One-to-one; onto 

 

Solve the problem.

15) The columns of  =  are  =  ,  =  ,  =  .

 

Suppose that T is a linear transformation from  into  such that

 

T( ) =  , T( ) =  , and T( ) = .

 

Find a formula for the image of an arbitrary x =  in .

 

A)

T =               B)

T = 

C)

T =           D)

T = 

 

16) The columns of  =  are  =  ,  =  ,  =  .

 

Suppose that T is a linear transformation from  into  such that

 

T( ) =  , T( ) =  , and T( ) = .

 

Find a formula for the image of an arbitrary x =  in .

 

A)

T =           B)

T = 

C)

T =               D)

T = 

 

Find the standard matrix of the linear transformation T.

17) T:  ->  rotates points (about the origin) through  π radians (with counterclockwise rotation for a positive angle).

 

A)

       B)

  C)

   D)

 

18) T:  ->  first performs a vertical shear that maps  into  + 3, but leaves the vector  unchanged, then reflects the result through the horizontal -axis.

 

A)

             B)

              C)

 D)

 

19) T:  ->  first performs a vertical shear that maps  into  + 5, but leaves the vector  unchanged, then reflects the result through the horizontal -axis.

 

A)

             B)

             C)

             D)

 

Determine whether the linear transformation T is one-to-one and whether it maps as specified.

20) Let T be the linear transformation whose standard matrix is

A = .

Determine whether the linear transformation T is one-to-one and whether it maps  onto .

 

A) One-to-one; not onto             B) Not one-to-one; not onto 

 

C) Not one-to-one; onto              D) One-to-one; onto 

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