Problem 8. PREVIEW ONLY -- ANSWERS NOT RECORDED Are the following statements true or false? 1. If W is a subspace of R" and if v is in both W and W¹, then v must be the zero vector. ? ? 2. If vectors V₁,..., Vp span a subspace W and if x is orthogonal to each V, for j = 1,..., p. then x is in W¹.
Problem 8. PREVIEW ONLY -- ANSWERS NOT RECORDED Are the following statements true or false? 1. If W is a subspace of R" and if v is in both W and W¹, then v must be the zero vector. ? ? 2. If vectors V₁,..., Vp span a subspace W and if x is orthogonal to each V, for j = 1,..., p. then x is in W¹.
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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Transcribed Image Text:Problem 8. PREVIEW ONLY -- ANSWERS NOT RECORDED
Are the following statements true or false?
?
?
?
?
1. If W is a subspace of R" and if v is in both W and W¹, then v must be the zero vector.
2. If vectors V₁,..., Vp span a subspace W and if x is orthogonal to each v, for j = 1,...,p, then x is in W¹
3. For all vectors u, v E R", we have uv-v.u
4. If W = Span{x₁, X2, X3} with {X1, X2, X3} linearly independent, and if {V₁, V2, V3} is an orthogonal set in W consisting of non-zero vectors, then {V₁, V2, V3} is an orthogonal basis for W.
5. The best approximation to y by elements of a subspace W is given by the vector y
projw (y).
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