SKIP Let T: R2 → R² be a linear transformation that first performs a horizontal shear that transforms e2 into e2 – 3 e and that does not change e, and then reflects each point through the line x1 = x2. Find the standard matrix A of T.

SKIP Let T: R2 → R² be a linear transformation that first performs a horizontal shear that transforms e2 into e2 – 3 e and that does not change e, and then reflects each point through the line x1 = x2. Find the standard matrix A of T.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 4E: The Standard Matrix for a Linear TransformationIn Exercises 1-6, find the standard matrix for the...

See similar textbooks

Related questions

Q: Find the standard matrix for the linear transformation T. T(x, y) = (3x + 4y, x – 8y)

Q: Let T be a linear transformation from R² to R? that satisfies T (| ) = 51 and T () = Find the…

A: It is given that, let T be a linear transformation from R2 to R2 that satisfies T1-1=23 and T01=-11…

Q: Find the standard matrix for the linear transformation T: R“ → R² that rotates points about the…

Q: Find the matrix A of the linear transformation from R to R' given by 5 T 6 x1 + -1 x2. %3D -8 7 A =

Q: let T: R2->R3 be a linear transformation such that T(e1)= -1 0 4 and T(e2)= -2 -1…

A: Let T: R2->R3 be a linear transformation and let A standard matrix for T, then A is matrix…

Q: Consider a linear transformation T from R³ to R² for which 3 8 T T %3D T %3D 6 Find the matrix A of…

Q: Choose the correct answer: The matrix representation of the linear transformation а T: R² → R³…

Q: Find the standard matrix for the linear transformation T:R? → R? that shears horizontally such that…

A: SolutionGivenThe linear tranformation T:ℝ2→ℝ2 that shears horizontally such that01→0.981and then the…

Q: Find the standard matrix for the linear transformation T. T(x, y) (3x + 4y, 3x - By) BE

Q: and let T: R-→R? be a linear transformation that maps x into x,v, +x,V,. Find a matrix A such that…

Q: Suppose T is a transformation from R2 to R2. Find the matrix A that induces T if T is reflection…

Q: Let T: R2→R2 be the linear transformation whose standard matrix is [1 1] [0 -1] Find an example…

A: Given problem is :

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

A: T:R2-> R2 is vertical shear transformation that is defined by...

Q: Determine the linear transformation T: R→ R? that has the given matrix 2 -1 5 A = 3 1 -2

Q: Find the standard matrix of the linear transformation T : R² → R² defined by T(x) = proj,x where the…

Q: Let T be the linear transformation defined by T(1, 2, 23, T4) = 8x1 + 3r2 + 7x4. Find its associated…

Q: Let T : R? → R² be given by 4 T(x) = x. Find the matrix M of the inverse linear transformation, T-1.…

A: Given that:T:ℝ2→ℝ2Tx→=45-50x→

Q: Consider the linear transformation T: R → R' given by [ 2х + 3у-z y x +2z х — 2у+ 4z Find the…

A: The standard basis of R3

Q: Find the standard matrix for the linear transformation 7. T(x, y, z) = (3x - 5z, 5y - z) ↓T

Q: Let T : R² → R² be a transformation. Which matrix, T, is a reflection over the у-аxis? 1 0 1 1 -1 -1

A: Let T:R2→R2 be a linear transformation. We have to find the matrix T, which is the reflection over…

Q: Let A = and B = 4 Find the matrix C of the linear transformation T(x) = B(A(x)). C =

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R?→R?, first performs a…

Q: Assume that T defines a linear transformation and use the given information to find the matrix of T.…

A: To find: Use the given information to find the the matrix of T

Q: Let A be the matrix representing the linear transformation T : R2 → R² defined by 2 2 What is the…

A: The objective is to find det(A)

Q: Find the standard matrix for the linear transformation T:R? → R? that contracts points horizontally…

Q: ([H) - 비 Suppose that T : R? → R? is a linear transformation and T and T (a) Find the standard…

Q: Suppose T is the transformation from R2 to R² that results from a rotation by t/2 followed by a…

A: T is a transformation from ℝ2 to ℝ2 that results from a rotation by π2 followed by a rotation by π.

Q: Suppose T is the transformation from R2 to R2 that results from a rotation by a/2 followed by a…

Q: Find the standard matrix of the linear transformation in the given attachement.

A: The given linear transformation is: Txyz=x+zy+zx+y

Q: Let T : R? → R² be the linear transformation that first reflects points through the x-axis and then…

Q: Write down the matrix A that represents the linear transformation ƒ : R² - (a) R² (i.e. so that f(x)…

Q: Find the standard matrix for the linear transformation T. T(X, y, z) (6x - 4z, 4y - z) D0

A: The given linear transformation T is, Tx,y,z=6x-4z,4y-z

Q: Find the standard matrix for the linear transformation T: R - R? that rotates points about the…

A: Find Transformation matrix T.

Q: Find the standard matrix for the linear transformation T.T(x, y) = (5x + y, 0, 4x − 5y)

Q: Consider the linear transformation T : R? → R defined by Т(х, у) —D (4х + 3у, —х + бу, —5х + 9у) If…

A: The given linear transformation T:ℝ2→ℝ3 defined by Tx,y=4x+3y, -x+6y, -5x+9y. If A is the standard…

Q: Find the matrix A of the linear transformation T from R? to R² that rotates any vector through an…

Q: Determine the matrix of the given linear transformation. T:R → R? defined by T(x, y) = (-2x+7y,5x-…

A: For the solution of the problem follow the next step.

Q: Find the standard matrix of the linear transformation T. T: R-> R first performs a vertical shear…

A: We have to solve given problem:

Q: Find the standard matrix for the linear transformation T.T(x1, x2, x3, x4) = (0, 0, 0, 0)

A: Let Now,

Q: Assume thatT is a linear transformation. Find the standard matrix of T. T: R2-R2, first performs a…

A: The solution are next step

Q: Let T : R? R2 be the linear transformation that first reflects points through the x-axis and then…

Q: Suppose T is a transformation from R2 to R2. Find the matrix A that induces T if T is reflection…

Q: Consider the linear transformation T: R" HR", and its associated matrix A = [T(ëi) T(ë») T(em)] E…

A: Given linear transformation T: Rm -> Rn

Q: Let T : R- –→ R² be the linear transformation whose standard matrix is 1 1 -1 Find an example of a…

Q: Consider a linear transformation T from R? to R² for which (E)- (A)-- and T Find the matrix A of T.…

Q: Find the standard matrix for the linear transformation T:R² → R² that rotates points about the…

A: Explanation of the answer is as follows

Q: Suppose that T : R² → R´ is a linear transformation obeying 4 (). 7 and 13 Find the standard matrix…

Q: Suppose T is a transformation from R2 to R2. Find the matrix A that induces T if T is reflection…

Q: 4) Given a linear transformation T: R² → R² is a vertical shear that maps e, into 2-e, but leaves e;…

A: The standard matrix or matrix of linear transformation is 0 0 2 1

Q: Give the standard matrix of the linear transformation T:R2→R2 that firstreflects points through the…

A: The reflection of point x1x2 along the line x2=x1 changes the co-ordinates to yield x2x1. The…

Question

SKIP
Finding the standard matrix
Let T : R² -→ R² be a linear transformation that first performs a horizontal
shear that transforms e2 into e2 – 3 e¡ and that does not change e1, and then
reflects each point through the line x1 = x2.
Find the standard matrix A of T.
A

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

The figure shows three outline versions of the letter F. The second one is obtained from the first by shrinking horizontally by a factor of 0.75, and the third is obtained from the first by shearing horizontally by a factor of 0.25. a Find a data matrix D for the first letter F. b Find a transformation matrix T that transforms the first F into the second. Calculate TD, and verify that this is a data matrix for the second F. c Find the transformation matrix S that transforms the first F into the third. Calculate SD, and verify that this is a data matrix for the third F.
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
The Standard Matrix for a Linear TransformationIn Exercises 1-6, find the standard matrix for the linear transformation T. T(x,y)=(5x+y,0,4x5y)
Finding the Standard Matrix and the Image In Exercise 11-22, a find the standard matrix A for the linear transformations T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the vector w=(3,1) in R2:T(v)=2projwvv, v=(1,4).
Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix over. With as defined in the preceding paragraph,
In Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[x+zy+zx+y]
In Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[xy+z2x+y3z]
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.
In Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 21. Clockwise rotation through 30° about the origin