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(1) A subset W in a vector space V in R³ is given by W = * = { u = ( ² ) [(x + y)² + 2³² = 0 } ₁ In R³, (x + y)² + z² = 0 is identical to x + y = 0 and z = 0, and accordingly, W is an intersection of subsets W₁ and W₂: W =W₁0W₂; = { u = ( ² ) |x + y = 0 } ; 2 = {₁ = ( ) |² = 9}. W₂ Prove that both W₁ and W₂ are subspaces of V. If so, W is also a subspace of V. W₁ = u =

(1) A subset W in a vector space V in R³ is given by W = * = { u = ( ² ) [(x + y)² + 2³² = 0 } ₁ In R³, (x + y)² + z² = 0 is identical to x + y = 0 and z = 0, and accordingly, W is an intersection of subsets W₁ and W₂: W =W₁0W₂; = { u = ( ² ) |x + y = 0 } ; 2 = {₁ = ( ) |² = 9}. W₂ Prove that both W₁ and W₂ are subspaces of V. If so, W is also a subspace of V. W₁ = u =

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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(1) A subset W in a vector space V in R³ is given by w = { u = ( ) [(x + y)² + z² = 0}. In R³, (x + y)² + z² = 0 is identical to x + y = 0 and z = 0, and accordingly, W is an intersection of subsets W₁ and W₂: W = W₁nW₂; 1 ² = { u = (²) |x + y = 0 } ; W₁ = W 2 v₂ = {μ = ( ² ) ² = 0}₁ u Prove that both W₁ and W₂ are subspaces of V. If so, W is also a subspace of V.
Transcribed Image Text:(1) A subset W in a vector space V in R³ is given by w = { u = ( ) [(x + y)² + z² = 0}. In R³, (x + y)² + z² = 0 is identical to x + y = 0 and z = 0, and accordingly, W is an intersection of subsets W₁ and W₂: W = W₁nW₂; 1 ² = { u = (²) |x + y = 0 } ; W₁ = W 2 v₂ = {μ = ( ² ) ² = 0}₁ u Prove that both W₁ and W₂ are subspaces of V. If so, W is also a subspace of V.
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