- #1

ElijahRockers

Gold Member

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## Homework Statement

Let V be the set of all ordered pairs of real numbers, with addition being defined as:

[itex](x_1 , x_2 ) + (y_1 , y_2 ) = (x_1 + y_1 , x_2 + y_2 )[/itex]

and scalar multiplication defined as:

[itex]\alpha \circ (x_1 , x_2 ) = (\alpha x_1 , x_2)[/itex]

Is V a vector space with these operations? Justify your answer.

## The Attempt at a Solution

I am thinking yes, because the scalar multiplication rule does not seem to violate any of the 8 axioms for vector spaces, but it seems wrong intuitively.