Question

Show that the vectors u₁ =(1,1,1), u₂ =(1,2,3), u₃ 3=(1,5,8) span R²

Answer 1

From the question above, we can see that $u_1,u_2,u_3 \in \R^3$. By definition of spanning sets of a vector space, the spanning set must be a subset of the vector space. But, $u_1,u_2,u_3 \not\in \R^2 \implies \{u_1,u_2,u_3\}\not\subset\R^2$. Hence $u_1,u_2,u_3$ does not spans $\R^2$