2b) Let P(x) = P2x² + P1x + po and ¶(x) = q2x² + q1ª + q0 polynomials from R=ls2•. Let be given the scalar product (-, ·)2 : R[r]<2 × R[c]<2 → R; {p, q)2 = p292 + 4p1q1 + p290 + Po92 + 2po90 1 bị (x) = x², b2(x) = x² – 1, b3(x) = from R[x]<2. R[c]<2. on the vector space R[r]<2• and the basis B = {b1, b2, b3} with (', -)2 Show that B is an orthonormal basis with respect to the scalar product of determine coordinate map KB with respect to B from Use this to
2b) Let P(x) = P2x² + P1x + po and ¶(x) = q2x² + q1ª + q0 polynomials from R=ls2•. Let be given the scalar product (-, ·)2 : R[r]<2 × R[c]<2 → R; {p, q)2 = p292 + 4p1q1 + p290 + Po92 + 2po90 1 bị (x) = x², b2(x) = x² – 1, b3(x) = from R[x]<2. R[c]<2. on the vector space R[r]<2• and the basis B = {b1, b2, b3} with (', -)2 Show that B is an orthonormal basis with respect to the scalar product of determine coordinate map KB with respect to B from Use this to
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.3: Proving Triangles Similar
Problem 41E: Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle...
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Q2b
I added orignal picture also with translated
![b) Es bezeichnen p(x) = p2x² + pix + po und q(x) = q2x² + q1x + qo Polynome aus R[x]<2.
Gegeben sei das Skalarprodukt
(:, -)2 : R[x]<2 × R[x]<2 → R; {p, q)2 =
P242 + 4p191 + P240 + po92 + 2po40
auf dem Vektorraum R[x]<2 sowie die Basis
1
B = {bi, b2, b3} mit bi (x) = x², b2(x) = x² – 1, b3(x)
= -x
2
des R[x]<2. Zeigen Sie, dass B eine Orthonormalbasis bezüglich (·, ·), des R[x]<2_ist.
Bestimmen Sie damit die Koordinatenabbildung Kg bezüglich B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09e3b736-76e8-44bc-9ba7-6988ba1bcf40%2F1a66f12d-a388-4381-a83f-1040a21f36de%2Fh1marq_processed.png&w=3840&q=75)
Transcribed Image Text:b) Es bezeichnen p(x) = p2x² + pix + po und q(x) = q2x² + q1x + qo Polynome aus R[x]<2.
Gegeben sei das Skalarprodukt
(:, -)2 : R[x]<2 × R[x]<2 → R; {p, q)2 =
P242 + 4p191 + P240 + po92 + 2po40
auf dem Vektorraum R[x]<2 sowie die Basis
1
B = {bi, b2, b3} mit bi (x) = x², b2(x) = x² – 1, b3(x)
= -x
2
des R[x]<2. Zeigen Sie, dass B eine Orthonormalbasis bezüglich (·, ·), des R[x]<2_ist.
Bestimmen Sie damit die Koordinatenabbildung Kg bezüglich B.
![2b) Let P(x) = P2a² + p1x + po and 9(x) = q2² + q1x + q0 polynomials from R-<2 . Let be given the scalar product
(', -)2 : R[x]<2 × R[x]<2 → R; (p, q)2
= P292 + 4p1q1 + P2¶o + p092 + 2po90
1
b1 (x) = x², b2(x) = x² – 1, b3(x) =
2" from R(x]<2.
R[r]<2•Use this to
on the vector space
R[2]<2.
and the basis
B = {b1, b2, b3}
with
Show that B is an orthonormal basis with respect to the scalar product of
(;, -) 2
from
determine coordinate
map
Кв with
respect to B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09e3b736-76e8-44bc-9ba7-6988ba1bcf40%2F1a66f12d-a388-4381-a83f-1040a21f36de%2Ft6azomo_processed.png&w=3840&q=75)
Transcribed Image Text:2b) Let P(x) = P2a² + p1x + po and 9(x) = q2² + q1x + q0 polynomials from R-<2 . Let be given the scalar product
(', -)2 : R[x]<2 × R[x]<2 → R; (p, q)2
= P292 + 4p1q1 + P2¶o + p092 + 2po90
1
b1 (x) = x², b2(x) = x² – 1, b3(x) =
2" from R(x]<2.
R[r]<2•Use this to
on the vector space
R[2]<2.
and the basis
B = {b1, b2, b3}
with
Show that B is an orthonormal basis with respect to the scalar product of
(;, -) 2
from
determine coordinate
map
Кв with
respect to B
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