Explanation Given information: The vertices are [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] . Calculation: First take the vertex [ 0 0 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 0 0 ] = [ 1 ⋅ 0 + 0 ⋅ 0 0 ⋅ 0 − 1 ⋅ 0 ] = [ 0 0 ] Then the matrix remains same as [ 0 0 ] . The obtained matrix [ 0 0 ] can be shown in Figure 1. Now, reflect the above graph about x axis and the resulted graph isshown in Figure 2. Now, take the matrix [ 0 0 ] as shown in Figure 1and use c = 2 in the transformation matrix [ c 0 0 1 ] to expand the vertex in the direction of x axis as, [ 2 0 0 1 ] [ 0 0 ] = [ 0 0 ] After expansion, the matrix remains same as [ 0 0 ] . Now, take the matrix [ 0 0 ] as shown in Figure 1and use c = 1 in the shear matrix [ 1 c 0 1 ] . After shear as, the matrix is obtained as, [ 1 1 0 1 ] [ 0 0 ] = [ 1 ⋅ 0 + 1 ⋅ 0 0 ⋅ 0 + 1 ⋅ 0 ] = [ 0 0 ] The obtainedmatrix remains same as [ 0 0 ] . Now, take the next vertex [ 1 0 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 1 0 ] = [ 1 ⋅ 1 + 0 ⋅ 0 0 ⋅ 1 − 1 ⋅ 0 ] = [ 1 0 ] Then the matrix remains same as [ 1 0 ] . The obtained matrix [ 1 0 ] can be shown in Figure 3. Now, reflect the above graph about x axis and the resulted graph is same as the initial graph as shown in Figure 3. Now, take the matrix [ 1 0 ] and use c = 2 in the transformation [ c 0 0 1 ] to expand the vertex in the direction of x axis as, [ 2 0 0 1 ] [ 1 0 ] = [ 2 ⋅ 1 + 0 ⋅ 0 0 ⋅ 0 + 1 ⋅ 0 ] = [ 2 0 ] After expansion, the matrix [ 1 0 ] becomes [ 2 0 ] as shown in Figure 4. Now, take the vertex [ 1 0 ] and use c = 1 in the shear matrix [ 1 c 0 1 ] such that the vertex is sheared as, [ 1 1 0 1 ] [ 1 0 ] = [ 1 ⋅ 1 + 1 ⋅ 0 0 ⋅ 1 + 1 ⋅ 0 ] = [ 1 0 ] After shear, the vertex remains same as [ 1 0 ] shown in Figure 3. Now, take the next vertex [ 1 1 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 1 1 ] = [ 1 ⋅ 1 + 0 ⋅ 1 0 ⋅ 1 − 1 ⋅ 1 ] = [ 1 − 1 ] Then the matrix becomes [ 1 − 1 ]

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 6, Problem 1P

To determine

To find:

The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 20T

Chapter 6, Problem 2P

Students have asked these similar questions

Set up the matrix which will perform the following transformation and write down its character.(x -y)to(y -x)

1) Derive the matrix that performs the following consecutive transformations(in augmented form):1- Translation of 2 units along x-axis.2- Rotation by 90° about z-axis.3- Rotation by 90° about y-axis.

I attached the image with the matrix where it asks to find For the linear transformation having the given matrix as its standard matrix, determine: a) domain, b) codomain, c) whether or not is onto, d) whether or not it is one to one thank you so much! [1 2 3 10] row 1 [2 5 5 23] row 2 [1 5 5 18] row 3 its like in the pic,

Chapter 6 Solutions

College Algebra

Ch. 6.1 - If a system of linear equations has infinitely...Ch. 6.1 - Write the augmented matrix of the following system...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Dimension of a Matrix State the dimension of the...Ch. 6.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The effect of the transformations on the vertices [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] of a square by sketching the graphs of the transformed vertices.

Solution Summary: The author analyzes the effect of the transformations on the vertices of a square by sketching the graphs.

Videos

To find:

The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

Want to see the full answer?

Chapter 6 Solutions

The effect of the transformations on the vertices [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] of a square by sketching the graphs of the transformed vertices.

Solution Summary: The author analyzes the effect of the transformations on the vertices of a square by sketching the graphs.

Videos

To find: The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

Want to see the full answer?

Chapter 6 Solutions

To find:

The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.