Symmetric bilinear form/Degeneracy space/Zero form/Exercise

Let ${}V$ be a finite-dimensional ${}K$-vector space, and let ${}\left\langle -,-\right\rangle$ denote a symmetric bilinear form on ${}V$. Show that the dimension of the degeneracy space is not necessarily the maximal dimension of a linear subspace with the property that the restricted form is the zero form.

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