0
$\begingroup$

Here $$ S=\left\{\begin{Vmatrix}x_1\\ x_2\end{Vmatrix}:x_1,x_2\in\mathbb{R}^n\right\} $$ and operations defined by equalities $$ \alpha\otimes\begin{Vmatrix}x_1\\ x_2\end{Vmatrix}=\begin{Vmatrix}\alpha x_1\\ \alpha x_2\end{Vmatrix}\qquad $$ $$ \begin{Vmatrix}x_1\\ x_2\end{Vmatrix}\oplus \begin{Vmatrix}y_1\\ y_2\end{Vmatrix}= \begin{Vmatrix}x_1+y_2\\ 0\end{Vmatrix} $$ My question: Is $\langle S, \oplus, \otimes\rangle$ a vector space?

  • 3
    Please put the entire question in the body of the post. Try and tell us what you tried or didn't try to do.2012-07-17
  • 3
    Also, please don't put things like "Prove your answer" in the title. The title is meant to show at a glance what the question is about. When you choose a title, imagine how it will look in the question list on the main page.2012-07-17
  • 2
    Is your addition commutative?2012-07-17

1 Answers 1