Matrices are fundamental in mathematics, computer science, and engineering. Here’s a concise guide to key operations:

📌 1. Matrix Addition

  • Rule: Add corresponding elements of two matrices with the same dimensions.
  • Example:
    A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
A + B = [[6, 8], [10, 12]]
matrix_addition

📌 2. Matrix Multiplication

  • Rule: Multiply rows of the first matrix by columns of the second matrix.
  • Example:
    A = [[1, 0], [0, 1]]  // Identity matrix
B = [[5, 6], [7, 8]]
A × B = [[5, 6], [7, 8]]
matrix_multiplication

📌 3. Transpose

  • Rule: Flip matrix over its diagonal, converting rows to columns and vice versa.
  • Example:
    A = [[1, 2], [3, 4]]
A^T = [[1, 3], [2, 4]]
matrix_transpose

📌 4. Determinant

  • Formula: For 2x2 matrix [[a, b], [c, d]], determinant = ad - bc.
  • Use Case: Used to determine invertibility of a matrix.

🔗 For deeper understanding, check our Linear Algebra Fundamentals tutorial.