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Archy [21]
3 years ago
10

"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axio

ms of vector spaces involving scalar multiplication v satisfies and which fail. for the ones it satisfies, prove that it satisfies the axiom. for those that fail, show that it fails with a counterexample."
Mathematics
1 answer:
expeople1 [14]3 years ago
5 0
Let \mathbf u\in\mathbb R^2, where

\mathbf u=(u_1,u_2)

and let k\in\mathbb R be any real constant.

Given this definition of scalar multiplication, we can see right away that there is no identity element e such that

e\mathbf u=\mathbf u

because

e\mathbf u=e(u_1,u_2)=(eu_1,0)\neq(u_1,u_2)=\mathbf u
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