The product of the given matrices can be defined and will be of the order 2 × 1. So the answer is option 2.
Explanation:
In order to multiply two matrices, the [tex]1^{st}[/tex] matrix must have the same number of columns as the rows in the [tex]2^{nd}[/tex] matrix. So to see if the given matrices can be multiplied we need to determine the order of both matrices.
The [tex]1^{st}[/tex] matrix has 2 rows and 3 columns. So the order of the [tex]1^{st}[/tex] matrix is 2 × 3.
The [tex]2^{nd}[/tex] matrix has 3 rows with 1 column. So its order is 3 × 1.
The [tex]1^{st}[/tex]matrix has 3 columnsand the [tex]2^{nd}[/tex] matrix has an equal number of rows, so they can be multiplied.
The order of the new matrix will be the [tex]1^{st}[/tex] matrix's number of rows × the [tex]2^{nd}[/tex] matrix's number of columns = 2 × 1.
