Matrix Multiplication Calculator
This Matrix Multiplication Calculator helps you multiply two matrices and shows each step clearly. In Algebra 2, matrix multiplication is used when working with matrices, systems, transformations, and organized numerical data. It works by taking a row from the first matrix and a column from the second matrix, multiplying corresponding entries, and adding the results to form each entry of the product matrix.
Step-by-step method
- Check the dimensions (Cols A must equal Rows B).
- Multiply row-by-column to get each entry.
Formula
Example 1: A (2×2) × B (2×2)
Step 1 - Check the dimensions (Cols A must equal Rows B).
In this problem: A is 2×2 and B is 2×2, so A × B is defined and will be 2×2.
1 | 2 |
3 | 4 |
5 | 6 |
7 | 8 |
Step 2 - Multiply row-by-column to get each entry.
In this problem: Each entry is a dot product of a row of A with a column of B.
1×5 + 2×7 | 1×6 + 2×8 |
3×5 + 4×7 | 3×6 + 4×8 |
19 | 22 |
43 | 50 |
Final answer:
19 | 22 |
43 | 50 |
Example 2: A (2×3) × B (3×2)
Step 1 - Check the dimensions (Cols A must equal Rows B).
In this problem: A is 2×3 and B is 3×2, so A × B is defined and will be 2×2.
2 | 0 | -1 |
3 | 1 | 4 |
1 | 2 |
0 | 5 |
-2 | 3 |
Step 2 - Multiply row-by-column to get each entry.
In this problem: Each entry is a dot product of a row of A with a column of B.
2×1 + 0×0 + (-1)×(-2) | 2×2 + 0×5 + (-1)×3 |
3×1 + 1×0 + 4×(-2) | 3×2 + 1×5 + 4×3 |
4 | 1 |
-5 | 23 |
Final answer:
4 | 1 |
-5 | 23 |
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