Question 1

Use the standard matrix for the linear transformation  defined by  to find the image of the vector  .

Accepted Answer

A)   
B)    
C)    
D)    
E)

Question 2

Use the function  to find the preimage of

Accepted Answer

A)  (-7, 4, t), where t is any real number 
B)  (4, -7, t), where t is any real number 
C)  (4, 7, t), where t is any real number 
D)  (-7, 4, 7) 
E)  (4, -7, 7)

Question 3

Find the standard matrix A for the linear transformation T where T is the projection onto the vector  in  .

Accepted Answer

A)    
B)    
C)    
D)    
E)

Question 4

The linear transformation   is represented by  , where  Find a basis for the range of T.

Accepted Answer

A)    
B)    
C)    
D)   
E)

Question 5

Find the matrix A' for T relative to the basis  .  ,

Accepted Answer

A)    
B)   
C)    
D)   
E)

Question 6

The linear transformation   is defined by  , where  Find

Accepted Answer

A)    
B)    
C)    
D)   
E)

Exam 6: Linear Transformations

Use the standard matrix for the linear transformation defined by to find the image of the vector .

Use the function to find the preimage of

Find the standard matrix A for the linear transformation T where T is the projection onto the vector in .

The linear transformation is represented by , where Find a basis for the range of T.

Find the matrix A' for T relative to the basis . ,

The linear transformation is defined by , where Find