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Let $V=\{(a,b) : (a,b) \in \mathbb{R}\}$

Is $V$ a vector space over $\mathbb{R}$ under:

Addition: $(a_1,a_2)+(b_1,b_2)=(a_1+b_2,a_2+b_1)$

$(a_1,b_1,a_2,b_2 \in\mathbb{R})$

Scalar multiplication: $t(a,b)=(ta,tb)$

$(t,a,b \in\mathbb{R})$

There exists an element $0$ so i think it's a vector space.

Am i right?

  • 2
    $(1,2)+(3,6)=(7,5)$; $(3,6)+(1,2)=(5,7)$. – 2017-01-14
  • 0
    i see... thank you. – 2017-01-14

0 Answers 0