Разложить вектор С=(8 , 9) по векторам A=(2 , -3) и B=(1 , 2)

Question

Разложить вектор С=(8 , 9) по векторам A=(2 , -3) и B=(1 , 2)

Answer 1

\ \left \{ {{m=8-2k} \atop {-3k+2(8-2k)=9}} \right. \ <=> \left \{ {{m=8-2k} \atop {-3k+16-4k=9}} \right. <=>\\\ \\\ <=> \left \{ {{m=8-2k} \atop {-7k=-7}} \right.<=> \left \{{{m=8-2k} \atop {k=1}} \right.<=> \left \{ {{m=8-2*1} \atop {k=1}} \right.<=> \left \{ {{m=6} \atop {k=1}} \right." alt=" \left \{ {{2k+m=8} \atop {-3k+2m=9}} \right. \ <=> \ \left \{ {{m=8-2k} \atop {-3k+2(8-2k)=9}} \right. \ <=> \left \{ {{m=8-2k} \atop {-3k+16-4k=9}} \right. <=>\\\ \\\ <=> \left \{ {{m=8-2k} \atop {-7k=-7}} \right.<=> \left \{{{m=8-2k} \atop {k=1}} \right.<=> \left \{ {{m=8-2*1} \atop {k=1}} \right.<=> \left \{ {{m=6} \atop {k=1}} \right." align="absmiddle" class="latex-formula">
c=a+6b