Question

базис линейного пространства V

Answer 1

Ответ:

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

Объяснение:

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

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