Imagine I have .
They give me a vector and they ask me to find another vector such that .
My attempt : I realized that can be written as a linear combination of and . (It's not always true I know, but it is in the particular example I got assigned)
So I must find a linear independent vector from but that spans with .
I don't know how to do it. (I'd be glad if there's a general method to find it)
Another question : say I found a vector and want to test if it spans with . If I see that I can write and as a combination linear of and the vector I found, does this implies that the latter 2 vectors span ?
P.S.: I've all the vectors if you want them... but I wanted to know the general case, hence my choice of using letters instead of numbers.