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If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) =< p, q>= aobo + a₁b₁ + a₂b₂ Investigate whether: a. = (symmetry) b. < (p+q),r>=+ (additive) c. = k < p, q> (homogeneous) d. < p,p>≥ 0 with < p,p>= 0 if and only if p = 0 (positive)

If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) =< p, q>= aobo + a₁b₁ + a₂b₂ Investigate whether: a. = (symmetry) b. < (p+q),r>=+ (additive) c. = k < p, q> (homogeneous) d. < p,p>≥ 0 with < p,p>= 0 if and only if p = 0 (positive)

Advanced Engineering Mathematics
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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If p = a₁ + a₁x + a₂x² and q = b₁ + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) =< p,q>= aobo + a₁b₁ + a₂b₂ Investigate whether: a. < p, q>=< q,p> (symmetry) b. < (p+q),r>=<p,r> + <q, r > (additive) c. < kp, q> = k < p, q> (homogeneous) d. < p,p>≥ 0 with < p,p>= 0 if and only if p = 0 (positive)
Transcribed Image Text:If p = a₁ + a₁x + a₂x² and q = b₁ + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) =< p,q>= aobo + a₁b₁ + a₂b₂ Investigate whether: a. < p, q>=< q,p> (symmetry) b. < (p+q),r>=<p,r> + <q, r > (additive) c. < kp, q> = k < p, q> (homogeneous) d. < p,p>≥ 0 with < p,p>= 0 if and only if p = 0 (positive)
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