Determine whether the set Wis a subspace of R³ with the standard operations. If not, state why. (Select all that apply.) W = {(x1, 1/X1, X3): X₁ and x3 are real numbers, x₁ # 0} OW is a subspace of R³. OW is not a subspace of R³ because it is not closed under addition. OW is not a subspace of R³ because it is not closed under scalar multiplication.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Determine whether the set Wis a subspace of R³ with the standard operations. If not, state why. (Select all that apply.)
W = {(x1, 1/X1, X3): X₁ and x3 are real numbers, x₁ # 0}
Wis a subspace of R³.
OW is not a subspace of R³ because it is not closed under addition.
OW is not a subspace of R³ because it is not closed under scalar multiplication.
Transcribed Image Text:Determine whether the set Wis a subspace of R³ with the standard operations. If not, state why. (Select all that apply.) W = {(x1, 1/X1, X3): X₁ and x3 are real numbers, x₁ # 0} Wis a subspace of R³. OW is not a subspace of R³ because it is not closed under addition. OW is not a subspace of R³ because it is not closed under scalar multiplication.
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