Let K={ [ a , b , c , ] ∈ R^3: 3a=5-c, 2a-3b+2c=0 } Is K a vector space? If K is a vect
Question: Let
\[K=\left\{ \left[ \begin{matrix} a \\ b \\ c \\ \end{matrix} \right]\in {{\mathbb{R}}^{3}}:\,\,3a=5-c,\,\,2a-3b+2c=0 \right\}\]Is K a vector space? If K is a vector space, then find a basis for K and find \(\dimK\).
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