Question

базис линейного пространства V

Answer 1

Ответ:

$\vec{a}=2\vec{p}+5\vec{q}$

Объяснение:

$\vec{p}=(2;-3), \ \vec{q}=(1;2) \\ \vec{a}=\alpha \vec{p}+\beta \vec{p} \\ (9;4)=\alpha (2;-3)+\beta (1;2) \\ (9;4)= (2\alpha;-3\alpha)+ (\beta;2\beta) \\ (9;4)=(2\alpha +\beta ;-3\alpha+2\beta ) \\ \\ \left\{\begin{matrix}2\alpha+\beta =9 \\ -3\alpha+2\beta =4 \end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}\beta =9-2\alpha \\ -3\alpha+2(9-2\alpha) =4 \end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}\beta =9-2\alpha \\ -3\alpha+18-4\alpha=4 \end{matrix}\right. \Leftrightarrow$

$\Leftrightarrow \left\{\begin{matrix}\beta =9-2\alpha \\ -7\alpha=-14 \end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}\beta =9-2*2 \\ \alpha=2 \end{matrix}\right. \Leftrightarrow \left\{\begin{matrix}\beta =5\\ \alpha=2 \end{matrix}\right.$