The product of two matrices [tex]X_{m\times{n}}[/tex] and [tex]Y_{n\times{r}}[/tex] equals a matrix [tex]M_{m\times{r}}[/tex], where the first element of the subscript represents the amount of files of the matrix and the second element represents the amount of columns of the matrix.
Then, in this case [tex]A_{1\times{3}}[/tex] [tex]B_{3\times{3}}[/tex], therefore, its product will result a matrix [tex]C_{1\times{3}}[/tex].
Because C matrix is going to have an only file and three columns, we now have to find the values of the elements in each column, based on the elements of A and B.
Commonly, to obtain the values of the resulting matrix, we just have to multiply each file of the first matrix by each column of the second matrix and sum, as follows:
