$1.$ Consider the pin$-$jointed system as shown above. For each bar, assume: EA $=1$ x $107$ N$.$

$($i$)$ Determine the global stiffness matrix formed from elements $1$ and $2.$

$($ii$)$ Determine the displacement at node $3,$ if the following loading and constraints are applied:

Nodes $1$ and $2$ constrained horizontally and vertically; Node $3$ constrained horizontally. An upward vertical load of $10000$ N applied at Node $3.$

$($iii$)$ Determine the displacement at node $3,$ if the following loading and constraints are applied:

Nodes $1$ and $2$ constrained horizontally and vertically; a horizontal force of $10000$ N in the positive x$-$direction applied at Node $3.$

PLEASE NOTE THAT YOU WILL HAVE TO SHOW AND DERIVE THE GLOBAL STIFFNESS MATRIX FORMED FROM ELEMENTS $1$ AND $2.$ CLEAR STEPWISE WORKING IS MUST IF NOT I WILL REPORT THE SOLUTION.