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Let V be the set of all ordered pairs of real numbers. Consider the following addition...

Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations V. Let u = (u1, u2) and v = (v1, v2).

• u ⊕ v = (u1 + v1 + 1, u2 + v2 + )

• ku = (ku1 + k − 1, ku2 + k − 1)

1)Show that the zero vector is 0 = (−1, −1).

2)Find the additive inverse −u for u = (u1, u2). Note: is not (−u1, −u2), so don’t write that.

3)Show that V is not a vector space.

Math   Advanced-Math   
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Answer #1

in part 3

It is satisfying all the properties of a vector space .

So it comes out to be a vector space.

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