Consider the function T : P2 (R) → P2(R) given by T(a + bx + cx²) = (a – 6+ c) + bx + (-6 – 2c)a². Let T be a linear transformation and eigenvalues of T are A = 1 and A= 2. Find a basis for E2(T) and the geometric multiplicity of A = 2.
Consider the function T : P2 (R) → P2(R) given by T(a + bx + cx²) = (a – 6+ c) + bx + (-6 – 2c)a². Let T be a linear transformation and eigenvalues of T are A = 1 and A= 2. Find a basis for E2(T) and the geometric multiplicity of A = 2.
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:Consider the function T : P2 (R) → P2(R) given by T(a + bx + cx²) = (a – 6+ c) + bx + (-6 – 2c)a².
Let T be a linear transformation and eigenvalues of T are A = 1 and A= 2.
Find a basis for E2(T) and the geometric multiplicity of A = 2.
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