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Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space...

Question

Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space...

Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in

Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): -1 1 ( 2 5 3 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, g(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2x2 matrices: (You'd decided what the inner product was on a previous math practice. Use your inner product again here). {{ : %][1 :] [: :][{ :) 1 1 1

Answers

361 A collection of basis & h, de..., daß is orthogonal if < Vish; >= 0 tisj & {1,2...m3, & itj Further, the basis is orthogm

We don't need to check for all vectors because even if for a pair of vector, if the condition doesn't hold then the basis is not orthogonal.


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