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et a be a fixed, unit length vector in 1R³. Define a linear transformation T: R³ - R²³ by T(x) = (a.x) a er. Describe the range of I in terms of the vector a and give the dimension of the rang Dureribe the Kernel of T in terms of the vector a and give the dimension of the Karnal b. Show that a is an eigenvector for T. What is the corresponding eigenvalue? C. Give the another distinct eigenverlue for I and explain how would you know it's. eigenvalue d. Find the dimension of the eigenspaces Ex for the eigenvalues just found. Is the standard matrix of T diagonalizable?

et a be a fixed, unit length vector in 1R³. Define a linear transformation T: R³ - R²³ by T(x) = (a.x) a er. Describe the range of I in terms of the vector a and give the dimension of the rang Dureribe the Kernel of T in terms of the vector a and give the dimension of the Karnal b. Show that a is an eigenvector for T. What is the corresponding eigenvalue? C. Give the another distinct eigenverlue for I and explain how would you know it's. eigenvalue d. Find the dimension of the eigenspaces Ex for the eigenvalues just found. Is the standard matrix of T diagonalizable?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 45E: Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a...
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be a fixed, uni't length vector in 1R³. Define a linear transformation T: R³ → R²³ by C Know it's et a T(x) = (α. x) a the vector and give the dimension of the rang cr. Describe the range of I in terms of the vector Describe the Kernel of T in terms of the vector a and give the dimension of the Kernel b. Show that is an expenvector for T. What is the corresponding eigenvalue? C. Give the another distinct eigenvalue for I and explain how would you eigenvalle d. Find the dimension of the eigenspaces Ex for the eigenvalues just found. Is the standard matrix of T diagonalizable?
Transcribed Image Text:be a fixed, uni't length vector in 1R³. Define a linear transformation T: R³ → R²³ by C Know it's et a T(x) = (α. x) a the vector and give the dimension of the rang cr. Describe the range of I in terms of the vector Describe the Kernel of T in terms of the vector a and give the dimension of the Kernel b. Show that is an expenvector for T. What is the corresponding eigenvalue? C. Give the another distinct eigenvalue for I and explain how would you eigenvalle d. Find the dimension of the eigenspaces Ex for the eigenvalues just found. Is the standard matrix of T diagonalizable?
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In part a, can you please help me describe the range and the kernel of T in geometric terms like if it's a line, plane,... ?

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