Introduction to 2D Arrays (Multidimensional Arrays) A 2D array is an array of arrays, often used to represent matrices or tables with rows and columns. It stores data in a grid-like structure, where each element can be accessed by two indices — one for the row and one for the column.
Declaration: int arr[rows][cols]; Access element at row i and column j: arr[i][j] Useful for matrix operations like addition, multiplication, transpose, and diagonal summation. Programs, Algorithms and Explanation
- Taking and Displaying a Fixed Size (3x3) Matrix Problem: Input and display a 3x3 matrix.
Algorithm:
Define matrix of size 3x3. Input matrix elements. Display matrix elements in row-column format. Explanation: Simple input-output of fixed-size matrix to practice basic 2D array handling.
- Matrix Addition Problem: Add two matrices of same dimensions.
Algorithm:
Input dimensions of both matrices (must be equal). Input elements of both matrices. Initialize result matrix. Loop through all elements and add corresponding elements. Display the resultant matrix. Explanation: Matrix addition is done element-wise and requires both matrices to have the same dimensions.
- Matrix Multiplication Problem: Multiply two matrices if number of columns in first matrix equals number of rows in second.
Algorithm:
Input rows and columns for both matrices. Check if multiplication is possible (cols1 == rows2). Input elements of both matrices. Initialize result matrix to zero. Multiply: for each element of result, sum products of row elements of M1 and column elements of M2. Display the result matrix. Explanation: Matrix multiplication combines rows of the first matrix with columns of the second, producing a new matrix.
- Matrix Transpose Problem: Find transpose of a matrix.
Algorithm:
Input rows and columns. Input matrix elements. Create transpose matrix with swapped dimensions. For each element (i,j), assign to transpose[j][i]. Display transpose. Explanation: Transpose flips rows and columns, which is used widely in matrix algebra and transformations.
- Sum of Diagonal Elements of a Matrix Problem: Calculate the sum of the main diagonal elements of a matrix.
Algorithm:
Input the number of the rows and columns. Check if the matrix is square (rows == cols). Input the matrix elements if it is a square matrix. Initialize a sum variable to 0. Loop through each row i and add the element at matrix[i][i] to the sum. Output the sum. Explanation:
The main diagonal of a matrix consists of elements where the row index and column index are the same (e.g., (0,0), (1,1), (2,2), ...). Summing these gives the diagonal sum.
These programs demonstrate foundational matrix operations using 2D arrays in C++. Understanding how to manipulate 2D arrays is crucial for solving complex problems involving matrices, including those in graphics, simulations, and data processing.
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