Question: Find a basis for the given subspaces of \({{R}^{3}}\) and \({{R}^{4}}\).

(a) All vectors of the form \(\left[ \begin{matrix}

a \\

b \\

c \\

\end{matrix} \right]\), where \(b=a+c\)

(b) All vectors of the form \(\left[ \begin{matrix}

a \\

b \\

c \\

\end{matrix} \right]\), where \(b=a\)

(c) All vectors of the form \(\left[ \begin{matrix}

a \\

b \\

c \\

\end{matrix} \right]\), where \(2a+b-c=0\)