Question

determine whether the products is defined or undefined. if defined, give the dimensions of the product matrix

Answer 1

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 $1^{st}$ matrix must have the same number of columns as the rows in the $2^{nd}$ matrix. So to see if the given matrices can be multiplied we need to determine the order of both matrices.
• The $1^{st}$ matrix has 2 rows and 3 columns. So the order of the $1^{st}$ matrix is 2 × 3.
• The $2^{nd}$ matrix has 3 rows with 1 column. So its order is 3 × 1.

• The $1^{st}$ matrix has 3 columns and the $2^{nd}$ matrix has an equal number of rows, so they can be multiplied.
• The order of the new matrix will be the $1^{st}$ matrix's number of rows × the $2^{nd}$ matrix's number of columns = 2 × 1.