Calc. Word Problem

[Robertinho!]

If u and v are nonzero and nonparallel vectors in the x-y plane, show that any vector in the plane can be written in the form au + bv, where a and b are appropriately chosen scalars.

 

[daon2]

If u and v are nonzero and nonparallel vectors in the x-y plane, show that any vector in the plane can be written in the form au + bv, where a and b are appropriately chosen scalars.

If they are not parallel, they are linearly independent. So [u v] is an invertible matrix (written as column vectors). Specifically, it is an onto map, so for all (x,y) in the plane, there is an (a,b) such that [u v](a,b) = (x,y).