Question 1

Find the standart matrix A for the linear transformation   defined by

Accepted Answer

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

Question 2

Find   where   and   by using the matrix relative to and   .

Accepted Answer

The image of each vector in B

Question 3

The linear transformation    is defined by   , where   Find

Accepted Answer

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

Question 4

Use the function   to find the image of

Accepted Answer

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

Question 5

The linear transformation   is defined by   , where   
Find ker(T).

Accepted Answer

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

Question 6

The linear transformation    is defined by   , where   Find the preimage of   .

Accepted Answer

A)     , where r, s, t are real numbers 
B)     , where r, s, t are real numbers 
C)     , where r, s, t are real numbers 
D)     , where r, s, t are real numbers 
E)     , where r, s, t are real numbers 
A)     , where r, s, t are real numbers 
B)     , where r, s, t are real numbers 
C)     , where r, s, t are real numbers 
D)     , where r, s, t are real numbers 
E)     , where r, s, t are real numbers

Question 7

Let   be the reflection in the line   . Find the image of the vector   .

Accepted Answer

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

Question 8

Find the image of the Z-shaped figure with vertices (0, 0), (6, 0), (6, 6), and (0, 6) under the transformation T which is the expansion and contraction represented by   .

Accepted Answer

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

Question 9

The linear transformation   is defined by   , where   Find range(T).

Accepted Answer

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

Question 10

Find the standard matrix A for the linear transformation T, where T is the counterclockwise rotation of 45° about the origin in   . Also use A to find   for the vector   .

Accepted Answer

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

Question 11

Let T be a linear transformation from   . Given that   , find nullity(T).

Accepted Answer

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

Question 12

Sketch the image of the rectangle with vertices at (0, 0), (0, 4), (1, 4), and (1, 0) under the transformation T which is the contraction given by   .

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Find the standard matrix A for the linear transformation T defined by   .

Accepted Answer

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

Question 15

Find the kernel of the linear transformation   , defined by   .

Accepted Answer

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

Question 16

Sketch the image of the unit square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1) under the transformation T which is the contraction given by   .

Accepted Answer

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

Question 17

Let   and   be bases for   , and let   be the matrix for   relative to B. The transition matrix P from B' to B is   . Use the matrices A and P to find   and   where   .

Accepted Answer

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

Question 18

Let   be a linear transformation such that     and   Find

Accepted Answer

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

Question 19

Find   where   and   by using the matrix relative to   and   .

Accepted Answer

The image of each vector in B

Question 20

Let   and   be bases for   . Find the transition matrix P from B' to B.

Accepted Answer

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

Find the standart matrix A for the linear transformation defined by

Find where and by using the matrix relative to and .

The linear transformation is defined by , where Find

Use the function to find the image of

The linear transformation is defined by , where Find ker(T).

The linear transformation is defined by , where Find the preimage of .

Let be the reflection in the line . Find the image of the vector .

Find the image of the Z-shaped figure with vertices (0, 0), (6, 0), (6, 6), and (0, 6) under the transformation T which is the expansion and contraction represented by .

The linear transformation is defined by , where Find range(T).

Find the standard matrix A for the linear transformation T, where T is the counterclockwise rotation of 45° about the origin in . Also use A to find for the vector .

Let T be a linear transformation from . Given that , find nullity(T).

Sketch the image of the rectangle with vertices at (0, 0), (0, 4), (1, 4), and (1, 0) under the transformation T which is the contraction given by .

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

Find the standard matrix A for the linear transformation T defined by .

Find the kernel of the linear transformation , defined by .

Sketch the image of the unit square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1) under the transformation T which is the contraction given by .

Let and be bases for , and let be the matrix for relative to B. The transition matrix P from B' to B is . Use the matrices A and P to find and where .

Let be a linear transformation such that and Find

Find where and by using the matrix relative to and .

Let and be bases for . Find the transition matrix P from B' to B.

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Exam 6: Linear Transformations

Find the standart matrix A for the linear transformation defined by

Find where and by using the matrix relative to and .

The linear transformation is defined by , where Find

Use the function to find the image of

The linear transformation is defined by , where Find ker(T).

The linear transformation is defined by , where Find the preimage of .

Let be the reflection in the line . Find the image of the vector .

Find the image of the Z-shaped figure with vertices (0, 0), (6, 0), (6, 6), and (0, 6) under the transformation T which is the expansion and contraction represented by .

The linear transformation is defined by , where Find range(T).

Find the standard matrix A for the linear transformation T, where T is the counterclockwise rotation of 45° about the origin in . Also use A to find for the vector .

Let T be a linear transformation from . Given that , find nullity(T).

Sketch the image of the rectangle with vertices at (0, 0), (0, 4), (1, 4), and (1, 0) under the transformation T which is the contraction given by .

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

Find the standard matrix A for the linear transformation T defined by .

Find the kernel of the linear transformation , defined by .

Sketch the image of the unit square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1) under the transformation T which is the contraction given by .

Let and be bases for , and let be the matrix for relative to B. The transition matrix P from B' to B is . Use the matrices A and P to find and where .

Let be a linear transformation such that and Find

Find where and by using the matrix relative to and .

Let and be bases for . Find the transition matrix P from B' to B.

Linear Equations

Matrices

Determinants

Vector Spaces

Inner Product Spaces

Eigenvalues Eigenvectors

Filters