Your Tasks

$1)$ Compute the system response $($unknown quantities$)$

Write the function solveSystem$()$ that takes six input arguments k$\_$pp$,$ k$\_$pf$,$ k$\_$fp$,$ k$\_$ff$,$ u$\_$p$,$ p$\_$f and returns two outputs u$\_$f and p$\_$p$.$

Input arguments:

k$\_$pp: a $2-$D NumPy array that represents the $$Kpp submatrix.

k$\_$pf: a $2-$D NumPy array that represents the $$Kpf submatrix.

k$\_$fp: a $2-$D NumPy array that represents the $$Kfp submatrix.

k$\_$ff: a $2-$D NumPy array that represents the $$Kff submatrix.

u$\_$p: a $1-$D NumPy array that stores the known prescribed displacement values $$Up$.$

p$\_$f: a $1-$D NumPy array that stores the known force values $$Pf$.$

Outputs:

u$\_$f: a $1-$D NumPy array that stores the displacement values of the free nodes $$Uf$.$

p$\_$p: a $1-$D NumPy array that stores the reaction forces on the prescribed nodes $$Pp$.$

Some things to consider:

Be aware of data types. What should the data type of u$\_$f and p$\_$p be$?$

You can use the @ character to represent matrix dot products. For example, $$A$$B can be expressed as A @ B in Python, where A$,$ B are NumPy arrays.