Answer
The forces at the four points are:
Point 1= 12N
Point 2= 1.5N
Point 3= 21.5N
Point 4= 12N
Work Step by Step
The flexibility matrix is given as;
$\mathbf{D} = \begin{bmatrix}.0040&.0030&.0010&.0005\\.0030&.0050&.0030&.0010\\.0010&.0030&.0050&.0030\\.0005&.0010&.0030&.0040\end{bmatrix}$
We are required to find the forces at the four points 1,2,3,4;
Deflections $\mathbf{y}$ at the four points are;
$\mathbf{y} = \begin{bmatrix}.08\\.12\\.16\\.12\end{bmatrix}$
Given that $\mathbf{y}=Df$
Then,
$\mathbf{f}=D^{-1}y$
Hence;
$\mathbf{f}
=\begin{bmatrix}.0040&.0030&.0010&.0005\\.0030&.0050&.0030&.0010\\.0010&.0030&.0050&.0030\\.0005&.0010&.0030&.0040\end{bmatrix} \begin{bmatrix}.08\\.12\\.16\\.12\end{bmatrix}$
$\mathbf{f}=\begin{bmatrix}12\\1.5\\21.5\\12\end{bmatrix}$
The forces are:
Point 1=12N
Point 2=1.5N
Point 3=21.5N
Point 4=12N
