Decide linear independence/Exercise

Decide whether the following vectors are linearly independent.

1. $(-1,1,-1)$, $(0,6,4)$, $(1,2,3)$, in the $ℝ$-vector space ${ℝ}^3$.
2. $1+\mathrm{i}$, $1+2\mathrm{i}$ in the $ℝ$-vector space $ℂ$.
3. $1+\mathrm{i}$, $1+2\mathrm{i}$ in the $ℂ$-vector space $ℂ$.
4. $1$, $\sqrt{3}$ in the $\mathbb{Q}$-vector space $ℝ$.

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