📊 Matrix Multiplication Tool
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📌 Understanding Matrix Multiplication
Matrix multiplication involves multiplying rows of Matrix A by columns of Matrix B:
- Matrix A must have the same number of columns as Matrix B has rows.
- The result is a new matrix where each element is the sum of the products of corresponding elements.
📌 Example Calculations
| Matrix A | Matrix B | Product |
|---|---|---|
| 1, 2; 3, 4 | 5, 6; 7, 8 | 19, 22; 43, 50 |
| 2, 4; 1, 3 | 3, 1; 5, 2 | 26, 10; 18, 7 |
🔧 Practical Applications of Matrix Multiplication
1. Computer Graphics: Used in 3D transformations and game physics.
2. Engineering & Physics: Helps in solving systems of linear equations.
3. Data Science: Essential for neural networks and AI computations.
❓ FAQs
Q1: How do I multiply two matrices?
✅ Multiply corresponding rows and columns, then sum the products.
Q2: What happens if the matrices are not compatible?
✅ Matrix multiplication is only possible when columns of Matrix A match rows of Matrix B.
Q3: Where is matrix multiplication used?
✅ It is widely used in **machine learning, physics, and graphics processing**.
Q4: Can I multiply non-square matrices?
✅ Yes! As long as the number of columns in Matrix A matches the number of rows in Matrix B.
Q5: How do I enter matrices correctly?
✅ Enter rows separated by semicolons **(e.g., 1,2;3,4 for a 2×2 matrix)**.