Product of Two Matrices

Product of Two Matrices

Let A be an m $\times$ n matrix and let B be an n $\times$ k matrix. To find the element in

the ith row and jth column of the product matrix AB, multiply each element in

the ith row of A by the corresponding element in the jth column of B, and then

add these products. The product matrix AB is an m $\times$ k matrix.

Example:-

A = $\begin{bmatrix} 2 & 3 &-1 \\ 4 & 2 & 2 \end{bmatrix}$ and B $\begin{bmatrix} 1\\ 8\\ 6 \end{bmatrix}.$

Then AB = $\begin{bmatrix} 2 & 2 & -1\\ 4 & 2 & 2 \end{bmatrix}\begin{bmatrix} 1\\ 8\\ 6 \end{bmatrix} = \begin{bmatrix} 20\\ 32 \end{bmatrix}$