Question

Se considea vectorii a vector= i vector + j vector ,b vector=2i vector-j vector si v vector=-4i vector+ 5 j vector.Determinati x,y pentru care v vector=xa vector +y b vector

Answer 1

a=i+j
b=2i-j
v=-4i+5j
-4i+5j=x(i+j)+y(2i-j)
-4i+5j=xi+xj+2yi-yj
Siastem
{-4=x+2y
{5=x-y scazi   relatia   1 din  2
5-(-4)=x-y-x-2y
5+4=-3y
9=-3y=.>y=9/(-3)=-3
Inlocuiesti   in  prima  relatie   si   obtii
-4=x+2*(-3)
-4=x-6
x=-4+6=2
x=2   y=-3