Let \(P = \{x^2+x,1\}\) and \(Q = \{x^2,x-1\}\). Is \(\operatorname{span}(P)=\operatorname{span}(Q)\) where the scalars are real numbers?
Yes
No
The answer is “No”.
For example, \(x^2\) in \(Q\) cannot be written as a linear combination of \(x^2+x\) and \(1\).