Maths puzzle involving vectors?

Find linear combinations of a=(2,2,4,0) b=(2,-1,3,1) c=(2,1,1,1) to form the vectors (1,0,3,0) and (0,1,0,2).

Maths puzzle involving vectors?
2a+2b+2c=1


therefore a+b+c=1 eq1


2a-b+c=1 eq2


b+c=2 eq3





substitute b+c=2 into eq1


a+2=1


a=-1





4a+3b+c=3 eq4


-4+3b+c=3


3b+c=7


we also know b+c=2





use these 2 eq to solve for b+7-3b=2


2b=5


b=2.5,c=-0.5


therefore the linear combination is -a+2.5b-0.5c