Question: how to find u in membership problem?

f1 = u1*f1 + u2*f2

f2 = u3*f1 + u4*f2

 

1. obviously u1 = 1 and u2 = 0 is solution, would like to see an exmaple which exist other solution?

2.

can it be seen as an matrix question such that matrix A := [u1, u2; u3, u4;];

or i should see them separately f1 = u1*f1 + u2*f2 and f2 = u3*f1 + u4*f2 ?

which Maple function calculate this?

3.

if want to determine whether [g1, g2] is member of [f1, f2], u1 = 1 and u2 = 0 can not be solution?

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