Linear algebra bilinear function

specialnlovin
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True or false. provide either a proof or counter example accordingly
if f is a function V\timesV\rightarrowk such that for all v,u,w\inV, \lambda\ink, f(\lambdav+u,w)=\lambdaf(v,w)+f(u,w). Then f is bilinear
I know that this does not include the second part of the requirement to be bilinear, however I cannot come up with a counter example. In order to find a counter example I know I should multiply a linear and non linear transformation but I cannot come up with one that disproves the statement.
 
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what about
f : \textbf{R}^{2} \times \textbf{R}^{2} \longrightarrow \textbf{R}
(u, v) \longmapsto u_{1}
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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