Chapter 8, Problem 8.5PE

(Algebra: add two matrices) Write a method to add two matrices. The header of the method is as follows:

public static double [][] addMatrix(double[] [] a , double[][] b)

In order to be added, the two matrices must have the same dimensions and the same or compatible types of elements. Let c be the resulting matrix. Each element c_ij is a_ij + b_ij. For example, for two 3 × 3 matrices a and b, c is

     $\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)+\left(\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right)=\left(\begin{array}{ccc}{a}_{11}+b_{11}& a_{12}+b_{12}& a_{13}+b_{13}\\ a_{21}+b_{21}& a_{22}+b_{22}& a_{23}+b_{23}\\ a_{31}+b_{31}& a_{32}+b_{32}& a_{33}+b_{33}\end{array}\right)$

Write a test program that prompts the user to enter two 3 × 3 matrices and displays their sum. Here is a sample run: