W = E R³ | a € R The set W is not a real vector space (vector space over R) under the standard operations of vector addition and scalar multiplication. Suppose u, v, w e W and c, d E R. 1. Which of the following axioms of vector addition are NOT satisfied for all u, v, w e W? O u+v€ W. O u+v= v + u. O (u+ v) + w = u+(v+w). O For every u E W, there exists 0 € W such that u + 0 = u.

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A: See the attachment

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Q: Linear Algebra

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Q: Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations:…

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A: The statement is true. We give the justification in the next step.

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Q: Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations:…

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A: note : The subpart (2) & (3) are same questions hence we will only answer the questions (1),…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.