Matrix Multiplication

Introduction: An $m \times n$ matrix is a rectangular array of numbers having $m$ rows and $n$ columns. The $(i, j)$ entry of $A$, located in the $i$th row and $j$th column of $A$, is denoted $A_{j}^{i}$. If $A$is an $m \times p$ matrix and $B$ is $p \times n$, then the product $AB$ has size $m \times n$, and $$ (AB)_{j}^{i} = \sum_{k=1}^{p} A_{k}^{i} B_{j}^{k}. $$

Instructions: Fill in the entries of the product, then check your answer. Use the tab key to navigate.

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Matrix sizes: