Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 5 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 3 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 5 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 3 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: In 3-dimensional plane. Describe in detail the following Shearing transformations in 3-dimensional…

A: We will use basic knowledge of 3-D calculus and linear algebra to answer this question.

Q: Find the standard matrix of the composite transformation from R2 to R2. Counterclockwise rotation…

Q: ] Given the following system of linear equations: Зх, + 4х, 1 2x, 2х, + X3 -1. 2.x, 2x, + 4x,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Q3: Map the straight line joining A(1+i2) and B (4+i) in the z-plane onto the w-plane using the…

A: Given, the straight line joining A(1+i2) and B(4+i) in the z-plane onto the w-plane using the…

Q: ) Find a linear transformation tak

A: Introduction: A linear transformation could be a operate from one vector house to a different that…

Q: Draw the shape of the following points {a(0,0), b(4,3), c(6,0),d(8,3),f(12,0)}, after that perform…

Q: Obtain an expression for a transformation matrix that will stretch a 3-D vector in x. Repeat for y.…

A: Let us consider an expression for a transformation matrix stretch a 3-D vector in x. 100→k00…

Q: Find the transformation matrix R that describes a rotation by 60° about an axis from the origin…

A: Given θ=60° and vector=1,1,1 So, the unit vector of the given vector is, ux=13uy=13uz=13

Q: If R = 2 4 4 2 R is the matrix of a linear transformation consisting of a rotation with angle e and…

A: Introduction: A linear transformation could be a function from one vector space to a different that…

Q: Find the Jacobian of the transformation x = 5u - 5v, y = u² – 2v —

A: Jacobian of transformation for two variable ∂x,y∂u,v=∂x∂udxdv∂y∂u∂y∂v ............(1)

Q: Find a single matrix for the transformation that is equivalent to doing the following four…

Q: Let T: R² → R2 be the linear transformation which first reflects in R² about the line y = x, and…

Q: (d) T: R² R³ where T 7[] þ I1 + 3x₂ 2x1 + 4x2 3x1 + 5x2

Q: For a linear transformation w= (atib)z, the point A= (1+j) in the z-plane was transformed to A' =…

Q: 2. Let a = 3 and 6 -4. (a) Graph the parallelogram spanned by a and b. Find if C' is matrix whose…

Q: 1.) Find the standard matrix for counterclockwise rotation of 210° about the origin in R2. Then use…

A: At first we find the rotation matrix for the transformation and then we find the new position of the…

Q: Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous…

A: To Determine :- The 3 × 3 matrix that produces the described composite 2D transformation below,…

Q: 2a + 56+c —а — 36 — 2с 3a + 76 +c -4a – 96 –c 2. T(а + bx + сх*). |

A: The objective is to write down the matrix of the given linear transformation withrespect to the…

Q: 11. Use matrix multiplication to show that two clockwise rotations of radians produces the same…

A: Let's denote the clockwise rotation matrix by R(theta), where theta is the angle of rotation in…

Q: a) Find the matrix of the linear transformation, 1 -3 x1 F( x2 ) + x2 -1 + x3 -2 = x1 4 -2 X3 b)…

Q: Write the 2 x 2 matriz representation of the given linear transformation and sketch the region…

A: T(x,y) = (1/4 * x, y) To find the matrix representation of this transformation, we need to apply it…

Q: Find the standard matrix for each linear transformation. Give on.

A: Given linear transformation T:R2→R2

Question

Find a single matrix for the transformation that is equivalent to doing the following four transformations of
the plane in succession:
1. Shear by a factor of 5 in the x-direction.
2. Reflection over the line y = x.
3. Expand by a factor of 3 in the y-direction.
4. Rotate counter-clockwise by 90 degrees.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Transformation$

Learn more about

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

Similar questions

Classify each transformation as a translation, a reflection, or rotation. Please complete all, thank you!
Let L be the line that passes through the origin in the direction of u = (1, 1, 1). Find the matrix for the rotation about L with angle 45 degree.
Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Translate by (7,4), and then rotate 30° about the origin. The 3x3 matrix is (Type an exact answer, using radicals as needed.)
Find the standard matrix of the given linear transformation from R² to R². Reflection in the line y = x
Q1. Consider the 3D shape with the following vertices: 4-38-60-60-98-88-8 A=5,B=5,C = 5,D = 5,E = 6,F= Rotate the 3D object by 30° (clockwise) at point D (fixed point) about the x-axis and then perform a uniform 1.5 scale. You should use rotation matrices.
Find the image of the point (x, y) under the matrix transformation that first reflects the point with respect to the x-axis, then rotates the resulting point about the origin through an angle of T/3, and then reflects the resulting point with respect to the line y = x.
Please solve all three parts
• √ √ (5² (5x+3y)dA where R is the parallelogram with vertices (0,0), (-1,-2), (-4,-3), and (-5,-5). Find Use the transformation =-u 4v, y=-2u - 3v 100
The linear transformation T: R R rotates points about the origin through - radians and then reflects through the horizontal z, axis. In this case, the standard matrix of T is
Show all work. Determine the Standard Matrix for the transformation rotating the plane counter- clockwise about the origin through 60°. 1 V3 1 1. A = -V3 1 1 -/3 2. А %3 2 V3 1 V3 1 3. А : V3 -1 V3 4. A = 1 -1 V3 -13 V3 1 5. А %3 1 1 V3 V3 -1 6. А %3D 2 1
Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Rotate points through 30° about the point (2,8). The 3x3 matrix is (Type an exact answer, using radicals as needed.)
Find the following, showing all working: (a) The matrix B that represents the linear transformation given by: first, a reflection over the line r = y; then, a clockwise rotation by 30° centred at 0. -5 2 (b) For the matrices A = 3 and C = 2B find the multiplication AC. 9 (c) The angle between and 3