Analyse the rigid$-$jointed frame illustrated below using the matrix stiffness method. Find the external reactions, and the moments and axial forces at the centre of each member. EI is $1000$kN$.$m$2$ and EA is $25000$ kN for the beam, and EI is $1500$ kN$.$m$2$ and EA is $35000$ kN for the columns. a $=3$ m$,$ b $=4$ m$,$ c $=5$ m$,$ and d $=2$ m$.$ w$1=12$ kN$/$m$,$ w$2=25$ kN$/$m$,$ P$1=12$ kN$,$ and P$2=18$ kN$.$ In addition, support A moves to the left by $7$ mm$,$ and support B settles vertically down by $12$ mm$.$