Let T : R → R° be a linear transformation.Let v,, v,, V3 be nonzero vectors in R’ such that:(T – 21)v,(T – 21)v,(T – 2I)v; = v2Prove that:(1) 1 = 2 is the only eigenvalue for T.(2) T is not diagonalizable.(3) Find a basis B for R' such that T(2 1 0`0 2 10 0 2,В

1) Given that v1, v2, v3 be nonzero vectors in ℝ3 such that T-2Iv1=0T-2Iv2=v1T-2Iv3=v2 That is,…

Let T : R → R° be a linear transformation. Let v,, v2, v3 be nonzero vectors in R' such that: (T – 21)v, = 0, (T – 21)v, (T – 2I)v3 = v2 %3| Prove that: (1) A = 2 is the only eigenvalue for T. (2) T is not diagonalizable. (3) Find a basis B for R such that T (2 1 0\ 0 2 1 0 0 2 B ||

Let T : R → R° be a linear transformation. Let v,, v2, v3 be nonzero vectors in R' such that: (T – 21)v, = 0, (T – 21)v, (T – 2I)v3 = v2 %3| Prove that: (1) A = 2 is the only eigenvalue for T. (2) T is not diagonalizable. (3) Find a basis B for R such that T (2 1 0\ 0 2 1 0 0 2 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

Let T : R → R° be a linear transformation.
Let v,, v,, V3 be nonzero vectors in R’ such that:
(T – 21)v,
(T – 21)v,
(T – 2I)v; = v2
Prove that:
(1) 1 = 2 is the only eigenvalue for T.
(2) T is not diagonalizable.
(3) Find a basis B for R' such that T
(2 1 0`
0 2 1
0 0 2,
В

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