## 2. Rayleigh-Ritz procedure (cont'd)

Thus, the boundary-value problem for a single element has been reduced to the solution of $$n$$ linear algebraic equations in $$n$$unknowns.

Equivalently, it has been reduced to a matrix equation with an $$n \times n$$ matrix.

If the element is a triangle, and each vertex has 1 degree of freedom, then the matrix will be 3×3. If each vertex has 3 degrees of freedom ($$x$$, $$y$$ and $$z$$ displacement components) then the matrix will be 9×9.

R. Funnell