Matrix Operations: Step-By-Step Multiplication Example

7. Example:

   $AB = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8\end{bmatrix} \begin{bmatrix}1 & 0 & 2 \\ 0 & 1 & 3\end{bmatrix} = \begin{bmatrix} c_{1,1} & c_{1,2} & c_{1,3} \\ c_{2,1} & c_{2,2} & c_{2,3}\\ c_{3,1} & c_{3,2} & c_{3,3}\\ c_{4,1} & c_{4,2} & c_{4,3} \end{bmatrix} = C$

   
   Explanation: First, we begin with an empty matrix $C_{4,3}$. We know that $C$ will be of this size since $A$ is of the size $4\times2$ and $B$ is of the size $2\times3$.
   The following slide contains an easy way of remembering what the dimensions of the resulting matrix are.