Decide linear independence/Exercise

Decide whether the following vectors are linearly independent.

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

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