linear algebra - Proof of $\mathcal{L}(V,W)$ is a vector space - Mathematics Stack Exchange

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Let $V$ be a vector space and $W$ be a subspace of $V .$ Def

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Let u= (U1 ,U2) and v= (V1,V2) be vectors in R^2 , we define: (u,v) =U1V1 - U2V2 + 3U3V2. How can you show that this gives an inner product on two

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