2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2a?, –1+r + x², 1 – x + x?}, {1– 3x + x², 1 – 3x – 2a², 1 – 2.x + 3r²} . В B' (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x2 + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix PBB'. (d) Verify that [x(p)]B' = PB-B' (x(p)B].
2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2a?, –1+r + x², 1 – x + x?}, {1– 3x + x², 1 – 3x – 2a², 1 – 2.x + 3r²} . В B' (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x2 + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix PBB'. (d) Verify that [x(p)]B' = PB-B' (x(p)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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Please do the number 2(b) math and give a short explanation of how you did it.
![2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider
В
{1+x – 2x², –1+x +x², 1 – x +
-
|
B'
{1- Зг + 2",1 — Зr — 2%, 1 — 2г + 3г"}.
3x – 2x2, 1 – 2x + 3.x²} .
(a) Show that B and B' are bases of P2(R).
(b) Find the coordinate matrices of p(x) = 9x² + 4x – 2 relative to the bases B and B'.
(c) Find the transition matrix PB→B'.
(d) Verify that
[x(p)]B' = PB¬B' [x(p)B].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89b773d6-6f0c-43c5-8497-4ca911f769a7%2F2350a66b-fb2a-4970-b95b-ffa3092633df%2Fyz1etnd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider
В
{1+x – 2x², –1+x +x², 1 – x +
-
|
B'
{1- Зг + 2",1 — Зr — 2%, 1 — 2г + 3г"}.
3x – 2x2, 1 – 2x + 3.x²} .
(a) Show that B and B' are bases of P2(R).
(b) Find the coordinate matrices of p(x) = 9x² + 4x – 2 relative to the bases B and B'.
(c) Find the transition matrix PB→B'.
(d) Verify that
[x(p)]B' = PB¬B' [x(p)B].
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