Consider the function T : P.(R) → P,(R) given by T(a + dz + cz²) = (a – b + c) + bz + (-b+2c)r² Find eigenvalues of T and state their algebraic multiplicity.
Consider the function T : P.(R) → P,(R) given by T(a + dz + cz²) = (a – b + c) + bz + (-b+2c)r² Find eigenvalues of T and state their algebraic multiplicity.
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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Would you please go thru the process of finding the values of T
![Consider the function T : P,(R) → P,(R) given by T(a + bz + cz³) = (a – 6+c) + bx + (-b+2c)z²
Find eigenvalues of T and state their algebraic multiplicity.
E Expand
Transcribed Image Text
Consider the function T:P2|R) - P2 (R) given by T(a+ bx + cx*) = (a - b+ c) + bx+ (-b+2c)x Find eigenvalues of Tand
state their algebralc multiplicity.
V Expert Answer
Step 1
Firstly we will find matrix associated with T.
Step 2
T: P, IR)→ P IR) grven by
Tla tbx+cx) = (a-b+s)+ bx+ Gb+2c) x?
To find eigen valuus of T we finst kind matrin
dtouated with wet: standoad. basis of
6 = {1, x,u²}.
T(4) = 1
T(x) = -I + x+(-1)x² = - 1+x-x2
T(x²) = 1 +ax?
T: B:8) - A= [1 -
O -1
Now, for eigen valuus of A we must caluulate
JA-AZ1=0.
*作。
=0.
=) d=1,1, 2.
) del P8 an eigen value with pmalgebraic multipiay2.
and d=2 s an
elgen value with algebraje mutipuicly](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16afeea3-ad60-4ec3-bf54-595dcafdf357%2F08ae62de-b867-4053-bd3b-59512da0853d%2F7vgyhua_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function T : P,(R) → P,(R) given by T(a + bz + cz³) = (a – 6+c) + bx + (-b+2c)z²
Find eigenvalues of T and state their algebraic multiplicity.
E Expand
Transcribed Image Text
Consider the function T:P2|R) - P2 (R) given by T(a+ bx + cx*) = (a - b+ c) + bx+ (-b+2c)x Find eigenvalues of Tand
state their algebralc multiplicity.
V Expert Answer
Step 1
Firstly we will find matrix associated with T.
Step 2
T: P, IR)→ P IR) grven by
Tla tbx+cx) = (a-b+s)+ bx+ Gb+2c) x?
To find eigen valuus of T we finst kind matrin
dtouated with wet: standoad. basis of
6 = {1, x,u²}.
T(4) = 1
T(x) = -I + x+(-1)x² = - 1+x-x2
T(x²) = 1 +ax?
T: B:8) - A= [1 -
O -1
Now, for eigen valuus of A we must caluulate
JA-AZ1=0.
*作。
=0.
=) d=1,1, 2.
) del P8 an eigen value with pmalgebraic multipiay2.
and d=2 s an
elgen value with algebraje mutipuicly
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