Answer
Deflections on points:
1=0.27 inch
2=0.30 inch
3=0.23 inch
Work Step by Step
Let D be the Flexibility Matrix in inches per pound
$D= \begin{bmatrix}.005&.002&.001\\.002&.004&.002\\.001&.002&.005\end{bmatrix}$
Forces of 30, 50, and 20 lb are applied at points 1,2, and 3 respectively.
$f= \begin{bmatrix}30\\50\\20\end{bmatrix}$
The corresponding deflections $y$ are,
$y=Df$
$y=\begin{bmatrix}.005&.002&.001\\.002&.004&.002\\.001&.002&.005\end{bmatrix}\begin{bmatrix}30\\50\\20\end{bmatrix}$
$y=\begin{bmatrix}(.005\times30)+(.002\times50)+(.001\times20)\\(.002\times30)+(.004\times50)+(.002\times20)\\(.001\times30)+(.002\times50)+(.005\times20)\end{bmatrix}$
$y=\begin{bmatrix}.27\\.30\\.23\end{bmatrix}$
Deflections on points:
1=0.27 inch
2=0.30 inch
3=0.23 inch
