Let v be a nonzero vector in R" and let V = Span{v}. Show that V has dimension n - 1. HINT:note that V¹ {XER" x = 0}. What sort of equation is v. x = √²x=0?Let {V1, V2,..=Vp} be an orthogonal set in R" and let a₁, a2,... , ap are scalars, show that2Σi=1рai vi||² = Σ|ai|²||vi||²2.i=1

Answered: Image /qna-images/answer/439f7736-b5eb-4f1c-b512-2b3307504966.jpg

Let ✓ be a nonzero vector in Rn and let V = Span{v}. Show that V has dimension n − 1. HINT: note that V¹ = { € R^|✔ · × = 0}. What sort of equation is ✔ · x = √²x = 0? Let {V1, V2, Vp} be an orthogonal set in R" and let a₁, a2,, ap are scalars, show that P ||Σa vi||² = |a|²||vi||2². αΐ i=1 i=1

Let ✓ be a nonzero vector in Rn and let V = Span{v}. Show that V has dimension n − 1. HINT: note that V¹ = { € R^|✔ · × = 0}. What sort of equation is ✔ · x = √²x = 0? Let {V1, V2, Vp} be an orthogonal set in R" and let a₁, a2,, ap are scalars, show that P ||Σa vi||² = |a|²||vi||2². αΐ i=1 i=1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 87E

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