kramtus51

2022-01-05

Find out if the set that can perform the specified operations is a vector space.

Identify the vector space axioms that are false for those that are not vector spaces.

the collection of all real numbers with addition and multiplication operations.

$\circ$ V is not a vector space, and Axioms 7,8,9 fail to hold.

$\circ$ V is not a vector space, and Axiom 6 fails to hold.

$\circ$ V is a vector space.

$\circ$ V is not a vector space, and Axiom 10 fails to hold.

$\circ$ V is not a vector space, and Axioms 6 - 10 fail to hold.

encolatgehu

Beginner2022-01-06Added 27 answers

Asume $({x}_{1},0),({x}_{2},0)\in V$

$R\propto \in \mathbb{R}$

$\Rightarrow ({x}_{1},0)+({x}_{2},0)=({x}_{1}+{x}_{2},0)\in V$

$R\propto ({x}_{1},0)=(\propto {x}_{1},0)\in V$

$\Rightarrow$ V is subspace of $\mathbb{R}}^{2$

$\Rightarrow$ V is vector space

karton

Expert2023-06-19Added 613 answers

star233

Skilled2023-06-19Added 403 answers

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?

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