[Math] Show that the vectors form a basis for $R^3$.

Question

Show that the vectors $\alpha_1 = (1, 0, 1)$, $\alpha_2 = (1, 2, 1)$, $\alpha_3 = (0, -3, 2)$ form a basis for $R^3$. Is it enough to show that the vectors are linearly independent?

Answer 1

Yes.

If the vector space has dimension $n$, then every set of $n$ independent vectors is a basis