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If $x+y=(x_1y_1, ..., x_ny_n)$ and $c\cdot '\ x=x^c_1, ..., x^c_n$, how to show that with these two operation $V$ is a subspace?
Let $V=(R^+)^n=\{(x_1, ..., x_n)| x_i\in R^+$for each $i\}$. In $V$ define a vector sum operation $+'$ by $x+y=(x_1y_1, ..., x_ny_n)$ and scalar multiplication $\cdot '$ by $c\cdot '\ x=x^c_1, ..., x^...
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