Determine whether the set W is a subspace of R° with the standard operations. If not, state why. (Select all that apply.) W = {(x1X2, X1 X2): x1 and x2 are real numbers} O w is a subspace of R. O w is not a subspace of R because it is not closed under addition. O w is not a subspace of R because it is not closed under scalar multiplication.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Determine whether the set W is a subspace of R° with the standard operations. If not, state why. (Select all that apply.)
W = {(x,X2, X1 X2): x1 and x2 are real numbers}
O w is a subspace of R3.
O w is not a subspace of R because it is not closed under addition.
O w is not a subspace of R3 because it is not closed under scalar multiplication.
Transcribed Image Text:Determine whether the set W is a subspace of R° with the standard operations. If not, state why. (Select all that apply.) W = {(x,X2, X1 X2): x1 and x2 are real numbers} O w is a subspace of R3. O w is not a subspace of R because it is not closed under addition. O w is not a subspace of R3 because it is not closed under scalar multiplication.
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