Let T : R → R° be a linear transformation. Let v,, v,, V3 be nonzero vectors in R’ such that: (T – 2I)v, = 0, (T – 21)v, (T – 21)v3 V2 | 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,, v,, V3 be nonzero vectors in R’ such that: (T – 2I)v, = 0, (T – 21)v, (T – 21)v3 V2 | 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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Transcribed Image Text: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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