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’

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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