Please do the number 2(d) 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. ConsiderВ{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].

We have B=1-1111-1-211 and B'=111-3-3-21-23 Also, matrix for p(x) will be xp=-249 First we will find…

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x - 2x?, –1+x +x²,1 – x + x²} , {1- Зг + д?, 1 — Зг — 21?, 1 — 2г + Зи?}. В |3D | 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 PB¬B'. (d) Verify that (x(p)]B' = PB¬B' [x(p) B]. %3D

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x - 2x?, –1+x +x²,1 – x + x²} , {1- Зг + д?, 1 — Зг — 21?, 1 — 2г + Зи?}. В |3D | 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 PB¬B'. (d) Verify that (x(p)]B' = PB¬B' [x(p) B]. %3D

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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Question

Please do the number 2(d) 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].

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