For each of the following linear operators on
(a) The transformation L that rotates each
(b) The transformation L that translates each point 3 units to the left and 5 units up.
(c) The transformation L that contracts each vector by a factor of one−third.
(d) The transformation that reflects a vector about the y−axis and then translates it up 2 units.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
Additional Math Textbook Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
Glencoe Algebra 2 Student Edition C2014
College Algebra with Modeling & Visualization (6th Edition)
Algebra: Structure And Method, Book 1
College Algebra Essentials (5th Edition)
College Algebra (10th Edition)
- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.arrow_forwardFind the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardFor the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the preimage of (0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn andRm. A=[0110]arrow_forward
- Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.arrow_forwardLet T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.arrow_forwardFor the linear transformation from Exercise 37, find a T(1,0,2,3), and b the preimage of (0,0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn and Rm. A=[012114500131]arrow_forward
- Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.arrow_forward1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .arrow_forwardLet T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning