matrices

Question

If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], then AB equals

RankGuru · Accepted Answer

1. **Multiplication Rule**: For $C = AB$, the element $c_{ij}$ is the dot product of the $i^{th}$ row of $A$ and the $j^{th}$ column of $B$.
2. **Calculation**:
   - $c_{11} = (1)(2) + (2)(1) = 4$
   - $c_{12} = (1)(0) + (2)(3) = 6$
   - $c_{21} = (3)(2) + (4)(1) = 10$
   - $c_{22} = (3)(0) + (4)(3) = 12$
3. **Result**: Matrix $AB = \begin{bmatrix} 4 & 6 \ 10 & 12 \end{bmatrix}$.

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