a) Number of elements and nodes,

b) Element matrix Equation is given by,

$\begin{bmatrix} K \end{bmatrix}^e=\frac{AE}{h_e}\begin{bmatrix} 1&-1\\ -1&1 \end{bmatrix}$

$For\,\, element \,\,1,\,\,A=250mm^2 \,\,,\,\, h_e=150mm$
$\frac{AE}{h_e}=\frac{250*2*10^5}{150}=333.33*10^3$
$\begin{bmatrix} K \end{bmatrix}^1=10^3\begin{bmatrix} 333.33&-333.33\\ -333.33&333.33 \end{bmatrix}$

$For\,\, element \,\,2,\,\,A=250mm^2 \,\,,\,\, h_e=150mm$
$\frac{AE}{h_e}=\frac{250*2*10^5}{150}=333.33*10^3$
$\begin{bmatrix} K \end{bmatrix}^2=10^3\begin{bmatrix} 333.33&-333.33\\ -333.33&333.33 \end{bmatrix}$

$For\,\, element \,\,3,\,\,A=400mm^2 \,\,,\,\, h_e=300mm$
$\frac{AE}{h_e}=\frac{400*2*10^5}{300}=266.67*10^3$
$\begin{bmatrix} K \end{bmatrix}^3=10^3\begin{bmatrix} 266.67&-266.67\\ -266.67&266.67 \end{bmatrix}$

c) Elemental matrix
$\begin{bmatrix} K \end{bmatrix}=10^3\begin{bmatrix} 333.33&-333.33&0&0\\-333.33&333.33+333.33&-333.33&0\\0&-333.33&333.33+267.67&-267.67 \\0&0&-267.67&267.67 \end{bmatrix}$

$\hspace{1cm}=10^3\begin{bmatrix} 333.33&-333.33&0&0\\-333.33&666.66&-333.33&0\\0&-333.33&600&-267.67 \\0&0&-267.67&267.67\end{bmatrix}$

d) Global Matrix Equation,
$\begin{bmatrix} K \end{bmatrix}\begin{Bmatrix} u \end{Bmatrix}=\begin{Bmatrix} P \end{Bmatrix}$
$ 10^3 \begin{bmatrix} 333.33&-333.33&0&0\\-333.33&666.66&-333.33&0\\0&-333.33&600&-267.67 \\0&0&-267.67&267.67\end{bmatrix}\begin{Bmatrix} u_1\\ u_2 \\u_3\\u_4 \end{Bmatrix}=\begin{Bmatrix} P_1 \\ P_2\\P_3\\P_4 \end{Bmatrix}$

Imposing boundary condition,
$u_1=0\,\,,\,\,u_4=0\,\,,\,\,P_2=300*10^3N$
$P_3=0\hspace{3cm}$ -for balancing,

Frame the equation,
$10^3(-333.33*u_2)P_1\hspace{8cm}$ -(1)
$10^3(666.66u_2-333.33u_3)=P_2=(300*10^3)\hspace{3.7cm}$ -(2)
$10^3(-333.33u_2+600u_3)=0\hspace{6.8cm}$ -(3)
$10^3(-267.67u_3)=P_4\hspace{8cm}$ -(4)

Solving equation (2) and (3) we get,
$\therefore \,\,\,u_2=0.623mm\hspace{2cm}u_3=0.346mm$
Substituting in equation (1) and (4), we get,
$P_1=-207.66kN \,\,\,P_4=92.61$
$\therefore \,\,\,F_1=-2000\,N$
$\sum P_x=o \hspace{3cm} $ -verified

Calculation for stress.
$\sigma^e=\frac{E}{h_e}\begin{bmatrix}-1&1 \end{bmatrix}\begin{Bmatrix} u_2^R\\ u_2^R \end{Bmatrix}$

For element 1,
$\sigma^1=\frac{2*10^5}{150}\begin{bmatrix}-1&1 \end{bmatrix}\begin{Bmatrix} 0\\ 0.623 \end{Bmatrix}$
$\sigma^1=830.67\,N/mm^2 \hspace{9cm}$ (Tensile)

For element 2,
$\sigma^2=\frac{2*10^5}{150}\begin{bmatrix}-1&1 \end{bmatrix}\begin{Bmatrix} 0.623\\0.346 \end{Bmatrix}$
$\sigma^2=-369.33\,N/mm^2 \hspace{8cm}$ (compressive)

For element 3,
$\sigma^3=\frac{2*10^5}{300}\begin{bmatrix}-1&1 \end{bmatrix}\begin{Bmatrix} 0.346&0 \end{Bmatrix}$
$\sigma^3=-230.67\,N/mm^2 \hspace{8cm}$ (compressive)

Calculation of strain,
Element 1, $\,\,\,e^1=\frac{\sigma^1}{E}=\frac{830.67}{2*10^5}=4.15*10^{-3}$

Element 2, $\,\,\,e^2=\frac{\sigma^2}{E}=\frac{369.33}{2*10^5}=1.846*10^{-3}$

Element 3, $\,\,\,e^3=\frac{\sigma^3}{E}=\frac{230.67}{2*10^5}=1.153*10^{-3}$