$\overrightarrow{a}=(2;4);\, \overrightarrow{b}=(-3;1);\, \overrightarrow{c}=(5;-2)$
a) Gọi $\overrightarrow{m}=(x_m;y_m)$
$\overrightarrow{m} = 2\overrightarrow{a} + 3\overrightarrow{b} - 5\overrightarrow{c}$
$\to \begin{cases}x_m = 2x_a + 3x_b - 5x_c\\y_m = 2y_a + 3y_b - 5y_c\end{cases}$
$\to \begin{cases}x_m = 2.2 + 3.(-3) - 5.5 = -30\\y_m = 2.4 + 3.1 - 5.(-2) = 21\end{cases}$
Vậy $\overrightarrow{m}=(-30;21)$
b) Gọi $\overrightarrow{n}=(x_n;y_n)$
$\overrightarrow{n}=24\overrightarrow{a} - 14\overrightarrow{c}$
$\to \begin{cases}x_n = 24x_a - 14x_c\\y_n = 24y_a - 14y_c\end{cases}$
$\to\begin{cases}x_n = 24.2 - 14.5 = -22\\y_n = 24.4 - 14.(-2) = 124\end{cases}$
Vậy $\overrightarrow{n}=(-22;124)$
