A remark about Galerkin method

In this article was proved, that any linear equation $Lu=f$ in the case of any linear versions of the Galerkin method, has at least as many unsolved right-hand sides in the form of linear combinations $f=L{\psi }_1+\mathrm{.}\mathrm{.}\mathrm{.}+L{\psi }_N+L{\psi }_{N+1}+\mathrm{.}\mathrm{.}\mathrm{.}+L{\psi }_{5N}+\mathrm{.}\mathrm{.}\mathrm{.}+L{\psi }_T$, as there are finite-dimensional linear subspaces with dimensionality as much than five times as the number of basis functions ${\psi }_1,\mathrm{.}\mathrm{.}\mathrm{.},{\psi }_N$ .