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

Question 5

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

Accepted Answer

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

Question 6

The linear transformation    is defined by   , where   Find

Accepted Answer

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

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

Linear Equations

Matrices

Determinants

Vector Spaces

Inner Product Spaces

Eigenvalues Eigenvectors

Filters

Exam 6: Linear Transformations