Symmetric bilinear form/Degeneracy space/Kernel to dual space/Exercise

Show that the degeneracy space of a symmetric bilinear form ${}\left\langle -,-\right\rangle$ on a ${}K$-vector space ${}V$ equals the kernel of the linear mapping

$V\longrightarrow {V}^{*},v\longmapsto \left\langle v,-\right\rangle .$

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