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
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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].
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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