Cho \(\vec a = \left( {2;\,\,1} \right),\vec b = \left( { - 3;\,\,4} \right),\vec c = \left( { - 4;\,\,9} \right)\).

* Hướng dẫn giải

\(\begin{array}{l}
m\vec a + n\vec b = \vec c\\
 \Leftrightarrow m\left( {2;1} \right) + n\left( { - 3;4} \right) = \left( { - 4;9} \right)\\
 \Leftrightarrow \left\{ \begin{array}{l}
2m - 3n =  - 4\\
m + 4n = 9
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
m = 1\\
n = 2
\end{array} \right.
\end{array}\)

\( \Rightarrow {m^2} + {n^2} = 5\)