We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x + 2y - z , -y + 4z ,5z) 1. Find standard matrix A of T 2. Find eigen values of A. 3. Find eigen vectors of A 4. Is A diagonalizable? Why? Find the diagonalized matrix of T in the base of eigen vectors B’. Specify B’

We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x + 2y - z , -y + 4z ,5z) 1. Find standard matrix A of T 2. Find eigen values of A. 3. Find eigen vectors of A 4. Is A diagonalizable? Why? Find the diagonalized matrix of T in the base of eigen vectors B’. Specify B’

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

We consider the linear transformation T : R3
------R
3
T(x,y,z) = ( x + 2y - z , -y + 4z ,5z)
1. Find standard matrix A of T
2. Find eigen values of A.
3. Find eigen vectors of A
4. Is A diagonalizable? Why?
Find the diagonalized matrix of T in the base of eigen vectors B’. Specify B’

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