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a) Determine the value of the scalar k so that the polynomials p(t)=t+k/8 and q(t)=−t2 are orthogonal. b) The vector subspace W ⊂ P2 generated by the vectors p(t)=4t−3 and q(t)=−t2 is the same generated by the polynomials of the previous item. Obtain a basis for W where the vectors are orthogonal and unitary.

a) Determine the value of the scalar k so that the polynomials p(t)=t+k/8 and q(t)=−t2 are orthogonal. b) The vector subspace W ⊂ P2 generated by the vectors p(t)=4t−3 and q(t)=−t2 is the same generated by the polynomials of the previous item. Obtain a basis for W where the vectors are orthogonal and unitary.

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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"In the vector space P2, of polynomials of degree less than or equal to 2, with real coefficients, consider the inner product defined by"
[image]
 
 
In relation to this inner product, answer the following items, mathematically justifying your statements.
a) Determine the value of the scalar k so that the polynomials p(t)=t+k/8 and q(t)=−t2 are orthogonal.
b) The vector subspace W ⊂ P2 generated by the vectors p(t)=4t−3 and q(t)=−t2 is the same generated by the polynomials of the previous item. Obtain a basis for W where the vectors are orthogonal and unitary.
in vector space P, of polynomials of degree less than or equal to 2, with real coefficients, consider the inner product defined by (p (t ), q(t)) = Só p ( t ) · q(t) dt and the norm associated with it, that is.|| p || = V{P (t),p(t)) Remember that a vector is said to be unitary if its norm is equal to one.
Transcribed Image Text:in vector space P, of polynomials of degree less than or equal to 2, with real coefficients, consider the inner product defined by (p (t ), q(t)) = Só p ( t ) · q(t) dt and the norm associated with it, that is.|| p || = V{P (t),p(t)) Remember that a vector is said to be unitary if its norm is equal to one.
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