Question

Разложить вектор с ={9;4} по векторам а={1;2} и b={2;-3}

Answer 1

c=ka+lb;
{9;4}={1;2}k+{2;-3}l;
{9;4}={k;2k}+{2l;-3l};
{9;4}={k+2l;2k-3l};

$left { {{k+2l=9} atop {2k-3l=4}} right;\ k=9-2l;\ 2(9-2l)-3l=4;\ 18-4l-3l=4;\ 18-7l=4;\ 7l=18-4;\ 7l=14;\ l=14:7;\ l=2;\ k=9-2*2=5;\ c=5a+2b$