Let's we're in vector space $E$ of dimension 3, and we have the basis $B_0 = (e1,e2,e3)$. I have another basis $B = (e1+e2, e1+e3, e2+e3)$. The problem asks me to give the coordinates of $e1,e2,e3$ "in the basis $B$". I'm not exactly sure what this means. I'm assuming this is what a "change of basis" is, but I'm not too sure.
I know that, if I create a matrix in which the column vectors are the vectors of $B$, then we have the "change of basis matrix", and right-multplying that matrix with a set of coordinates of a vector in basis $B$ with get me the coordinates in the canonical base, right? However, I'm not sure how to apply this knowledge to this particular problem. Any help is appreciated, thanks!