Разложить вектор  с= {3, 6} по векторам  а= {5, 4} и  b= {1, -1}. ПО Базису!  

[latex]c=xa+yb\\c=3i+6j\\\\a=5i+4j\\xa=x(5i+4j)=x5i+x4j\\\\b=i-j\\yb=y(i-j)=yi-yj\\\\c=(x5i+x4j)+(yi-yj)=(x5i+yi)+(x4j-yj)=\\=(5x+y)i+(4x-y)j\\c=3i+6j\\\\ \left \{ {{5x+y=3} \atop {4x-y=6}} \right.[/latex] [latex]5x+4x=9\\x=1\\\\5x+y=3\\5*1+y=3\\y=3-5\\y=-2\\\\c=1*a+(-2)*b=a-2b [/latex]