# I'm trying to complete the following exercise: Let V be the set of vectors (x_1,x_2,x_3,x_4) in RR^4 such that 2x_1−3x_2−x_3+x_4=0 x_1−x_2+2x_3−x_4=0 Show that V is a subspace of RR^4 and find a basis for V.

I'm trying to complete the following exercise:
Let V be the set of vectors $\left({x}_{1},{x}_{2},{x}_{3},{x}_{4}\right)\in {\mathbb{R}}^{4}$ such that
$2{x}_{1}-3{x}_{2}-{x}_{3}+{x}_{4}=0$
${x}_{1}-{x}_{2}+2{x}_{3}-{x}_{4}=0$
Show that V is a subspace of ${\mathbb{R}}^{4}$ and find a basis for V.
I already showed that V is a subspace of ${\mathbb{R}}^{4}$, but I'm having trouble finding a basis for V. Any help is welcome
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Hector Hamilton
Actually, even more is true. For $p>0$ and $q>0$, we have that
$\underset{x\to \mathrm{\infty }}{lim}\frac{{\mathrm{log}}^{p}x}{{x}^{q}}=\underset{x\to \mathrm{\infty }}{lim}\left(\frac{\mathrm{log}x}{{x}^{q/p}}{\right)}^{p}=\left(\underset{x\to \mathrm{\infty }}{lim}\frac{\mathrm{log}x}{{x}^{q/p}}{\right)}^{p}=\left(\underset{x\to \mathrm{\infty }}{lim}\frac{1}{\left(q/p\right){x}^{q/p}}{\right)}^{p}=0$
using continuity and l'Hôpital's rule.