$($Algebra: add two matrices$)$

Write a function to add two matrices. The header of the function is:

def addMatrix$($a$,$ b$)$:

In order to be added, the two matrices

and

must have the same dimensions and the same or compatible types of elements. Let

be the resulting matrix. Each element

is equal to

$.$ For example, for two $3$ by $3$ matrices and

and

$,$

is:

Write a test program that prompts the user to enter two matrices and displays their sum. The numbers in each matrix are entered in one line. Here is a sample run:

Sample Run

Enter matrix$1$: $123456789$

Enter matrix$2$: $02414\mathrm{.}52\mathrm{.}21\mathrm{.}14\mathrm{.}35\mathrm{.}2$

The matrices are added as follows:

$1\mathrm{.}02\mathrm{.}03\mathrm{.}00\mathrm{.}02\mathrm{.}04\mathrm{.}01\mathrm{.}04\mathrm{.}011\mathrm{.}0$

$4\mathrm{.}05\mathrm{.}06\mathrm{.}0+1\mathrm{.}04\mathrm{.}52\mathrm{.}2=5\mathrm{.}011\mathrm{.}58\mathrm{.}2$

$11\mathrm{.}08\mathrm{.}011\mathrm{.}01\mathrm{.}14\mathrm{.}35\mathrm{.}28\mathrm{.}112\mathrm{.}314\mathrm{.}2$