7. Let be the operator on P[r]3 defined by L(p(x)) = xp'(x) +p"(x) (1) Find the matrix A representing with respect to [1, x, x²]. (2) Find the matrix B representing with respect to [1, x, 1 + x²]. (3) Find the matrix S such that B = S-¹AS.
7. Let be the operator on P[r]3 defined by L(p(x)) = xp'(x) +p"(x) (1) Find the matrix A representing with respect to [1, x, x²]. (2) Find the matrix B representing with respect to [1, x, 1 + x²]. (3) Find the matrix S such that B = S-¹AS.
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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![7. Let be the operator on P[r]3 defined by
L(p(x)) = xp'(x) +p"(x)
(1) Find the matrix A representing with respect to [1, x, x²].
(2) Find the matrix B representing with respect to [1, x, 1 + x²].
(3) Find the matrix S such that B S-¹ AS.
(4) If p(x) = ao + a₁x + a₂(1 + x²),
=
calculate L¹ (p(x)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31ca2837-4270-45c6-8f74-bc32489909cd%2Ff94b236e-2586-40e9-98ca-ad8fa8da1f46%2F6k072bp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Let be the operator on P[r]3 defined by
L(p(x)) = xp'(x) +p"(x)
(1) Find the matrix A representing with respect to [1, x, x²].
(2) Find the matrix B representing with respect to [1, x, 1 + x²].
(3) Find the matrix S such that B S-¹ AS.
(4) If p(x) = ao + a₁x + a₂(1 + x²),
=
calculate L¹ (p(x)).
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