To implement Java program using Array.

Explanation

This Java program is designed to perform two fundamental linear algebra operations: Matrix Addition and Matrix Multiplication. The code is structured modularly, using helper methods to handle specific tasks like reading input, printing data, and performing mathematical calculations.

1. Input and Dimension Check: The program starts by asking the user for the number of rows and columns for two matrices, Matrix A and Matrix B. It performs a basic check to ensure dimensions are positive integers.
2. Modular Reading: The readMatrix method uses nested for loops to populate a 2D array. It prompts the user for each specific element (e.g., A[1][1]) to make the data entry process clear.
3. Addition Logic: Matrix addition is only possible if both matrices have the same dimensions ($rA=rB$ and $cA=cB$). The addMatrices method iterates through every index $(i, j)$ and computes the sum of the corresponding elements from A and B.
4. Multiplication Logic: Matrix multiplication has a stricter requirement: the number of columns in the first matrix ($cA$) must equal the number of rows in the second matrix ($rB$). The multiplyMatrices method uses a triple-nested loop:
   • The outer two loops ($i$ and $j$) navigate the resulting product matrix.
   • The innermost loop ($k$) performs the "dot product" of the $i$-th row of A and the $j$-th column of B.
5. Output: Finally, the program prints the original matrices and the results of the operations, provided the mathematical conditions for those operations were met.

Algorithm

1. Start.
2. Input Dimensions: Accept rows ($r$) and columns ($c$) for Matrix A and Matrix B.
3. Validation: If any dimension is $\le 0$, display "Invalid dimensions" and terminate.
4. Data Entry: Use nested loops to input elements for Matrix A and Matrix B.
5. Matrix Addition:
   • Check if $rA == rB$ and $cA == cB$.
   • If true, create a new matrix sum. For each index $(i, j)$, set sum[i][j] = A[i][j] + B[i][j].
   • If false, display a dimension mismatch error.
6. Matrix Multiplication:
   • Check if $cA == rB$.
   • If true, create a new matrix product of size $rA \times cB$.
   • For each row $i$ in A and each column $j$ in B, calculate the sum of products: product[i][j] += A[i][k] * B[k][j] where $k$ ranges from $0$ to $cA-1$.
   • If false, display an invalid dimensions error.
7. Display: Print the resulting matrices in a grid format.
8. Stop.