Question

Determine whether each matrix product is defined. If so, state the dimensions of the product.

$A_{2\times 3}·B_{3\times 2}$

Short answer

Matrix product of given matrices is defined.

Product matrix has 2 rows and 2 columns.

Step-by-step solution

- Write condition for matrix product to be defined.

For two matrices $A$ and $B$, the product $A·B$ is defined when number of columns of matrix $A$ is equal to the number of rows of matrix $B$.

- Write dimensions of given matrices

Matrix $A$ has 2 rows and 3 columns and matrix $B$ has 3 rows and 2 columns.

- Check multiplication is defined or not

As, number of columns of matrix $A$ is equal to the number of rows of matrix $B$.

So multiplication is defined.

- Write dimension of product matrix

When multiplication is defined then resultant matrix $A·B$ has number of rows equal to the number of rows of matrix $A$ and its number of column is equal to the number of columns of matrix $B$

So product of given two matrices gives a matrix which has 2 rows and 2 columns.