$(20$ points$)$ The mesh and boundary conditions below are for a $2-$D elastostatics problem. Following the method given in section $2\mathrm{.}7$ of the class notes, determine the NodeType matrix, NodeLabel matrix and G vector for the mesh shown below subjected to the following essential boundary conditions: The vertical edge $($nodes $1,2)$ can not move in either direction $($both components of the displacement are equal to zero$).$ The horizontal edge $($nodes $9,10)$ has a prescribed vertical displacement of $0\mathrm{.}05.$ Nodes are marked with a solid circle $($there are $8$ corner nodes and $2$ edge nodes$).$ Element numbers are circled.

Given the following element connectivity $($order of nodes for the elements$)$:

Element $1,$ nodes $10,9,7,8$

Element $2,$ nodes $8,7,5$

Element $3,$ nodes $8,5,6$

Element $4,$ nodes $2,6,5,1,4,3$

Determine the EleDofType matrix and EleDofLabel matrix for the $4$ elements. For each term in the element stifness matrix for element $1,$ indicate the corresponding location in the global stiffness matrix, or force vector, in the global system to which it will contribute.