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 + a₂b₂Investigate whether:a. < p, q>=< q,p> (symmetry)b. < (p+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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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)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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