Do the number 2(a) math and after that give a short explanation as a comment 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].

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Description: Do the number 2(a) math and after that give a short explanation as a comment 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 –

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2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x - 2x², –1+x+x², 1 – x + x²}, {1– 3x + x²,1 – 3x – 2x2, 1 – 2.x + 3x²} . B | | B' %3D | (a) Show that B and B' are bases of P2(R).

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x - 2x², –1+x+x², 1 – x + x²}, {1– 3x + x²,1 – 3x – 2x2, 1 – 2.x + 3x²} . B | | B' %3D | (a) Show that B and B' are bases of P2(R).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 34E

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Do the number 2(a) math and after that give a short explanation as a comment 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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