The linear transformation T(x) = Ax scales a vector x = in R? by 200% in the horizontal direction and 500% in the vertical direction, then rotates the vector 90° clockwise. Determine the standard matrix A of this transformation. 2 1 -1 5 0 5 0 2 2 -5 (A) A= (B) A= (C) A= (D) A= -2 0 -5 0

The linear transformation T(x) = Ax scales a vector x = in R? by 200% in the horizontal direction and 500% in the vertical direction, then rotates the vector 90° clockwise. Determine the standard matrix A of this transformation. 2 1 -1 5 0 5 0 2 2 -5 (A) A= (B) A= (C) A= (D) A= -2 0 -5 0

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: ] 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: 981. X-2 0 0 −1 1 - 2 0 0 −1 X-2,

A: The given matrix is; [lamda-2 -1 0 0 lamda-2…

Q: - 4 V, = X2 and v2= 7 and let T: R2-→R? be a linear transformation that maps x into x,v, + X,V2.…

A: That's easy. Have a great day!!!

Q: If T: R² R² is a linear transformation such that then the standard matrix of T is A = 16 2 17 T…

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: Quadrilateral ABC

A: Given: Quadrilateral A′B′C′D′ is obtained by transforming quadrilateral ABCD about the origin. To…

Q: Find the standard matrix of the linear transformations describes as Reflection around x-axis…

A: When we reflect a point about x- axis , x coordinate remains same , and sign of y-coordinate changes…

Q: Let's continue simulating the process of constructing a matrix for a 3D transformation that rotates…

Q: 2. Let A be the standard matrix of the linear transformation which rotates every vector in R²…

A: Bartleby Guideline : ''Since you have posted multiple questions ,we will provide the solution only…

Q: Find the standard matrix of the linear transformation T that rotates the plane clockwise through an…

Q: (a) find the standard matrix A for the linear transformation T, (b) use A to find the image of the…

A: We find the matrix A so that v , Av are 2x1 matrices.

Q: Suppose that T : R² → R² is a matrix transformation and that 7([}))-[-), "([;))-}] 7((:) (a) Find…

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

Q: Linear transformation on R2 consists first on flipping the y-y and then counterclockwide rotation by…

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R² R² first rotates…

Q: A linear transformation T: R² R2 first reflects points through the r-axis and then reflects the…

A: (b) Given transformation T:R2→R2 (i) The purpose is to find the matrix of the transformation. 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: a) Find the matrix of the linear transformation, 1 -3 x1 F( x2 ) + x2 -1 + x3 -2 = x1 4 -2 X3 b)…

Q: Write down the 2 × 2 matrices that represent the following linear transformations ofthe plane. Also…

A: As per guidelines, we will solve first three subparts of the question only. a) We have to find the…

Q: Write the transformation matrix for a R2 R2 linear transformation that rotates points 135° about the…

Q: 6. Consider the linear transformation V : R2 → R2 that reflects over the x-axis. a. On the axes…

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

A: Given linear transformation T:R2→R2

Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

Q: [11 ] Given the following system of linear equations: 3x, + 4x, = 2х, 2х, + X3 = -1. 2x, x, - 2x, +…

A: "Since you have posted a question with multisubparts, we will solve first 3 parts for you. To get…

Q: Describe what the linear transformation determined by the matrix A = [18] does to the square with…

A: As per the question we are given a linear transformation in terms of the transformation matrix A.…

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

A: The objective is to find the 3×3 matrix that produce the described composite 2D transformation using…

Q: Using the following 3 linear transformations, find their matrices: g(x, y) = (7x, 2y)…

Question

The linear transformation T(x) = Ax scales a vector x =
in R? by 200% in the horizontal
direction and 500% in the vertical direction, then rotates the vector 90° clockwise. Determine the
standard matrix A of this transformation.
(A) A=
(1) A- [ 3]
(C) A= [ 3]
2 1
0 5
0 2
2 -5
(D) A=
5
-1 5
2 0
2

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

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.
Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.
(c) Find the rotation matrix of a linear transformation T: R² R², which first rotates points 3 clockwise and then reflects points through the z-axis. -
Find the matrix for the given linear transformation. 180◦ rotation of R3 around the line spanned by (1, −1, 0) (All the process and steps)
Please solve all three parts
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.)
-2 Use a rectangular coordinate system to plot u = ,v = 1, and their images under the 4 -1 given transformation T(x) = | Describe geometrically what T does to each vector in R2.
I need help with this problem whats going in the blank
Find the matrix A of the linear transformation T from R2 to R² that rotates any vector through an angle of 150° in the clockwise direction. A =
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.