This question is about finding the basis of a span. I know that it should be the maximum linearly-independent subset of the given span but couldn't find a way to show that. The question is: find the basis of the span of $\{x, x^2, e^x, e^{x+1}\}$ in the space of functions from $\mathbb R$ to $\mathbb R$.
2026-04-07 04:40:39.1775536839
Linear Algebra: Basis/Span
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We have $e^{x+1}=e(e^x)$ so we we can eliminate $e^{x+1}$. To check the others are linearly independent use the Wronskian, if there does exist some $x \in \mathbb{R}$ such that the Wronskian is not zero, then $x,x^2,e^x$ are linearly independent.