Questions: The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist. A is 5 x 3, and B is 3 x 5. Find the size of the product AB. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The size of product AB is . B. The product AB does not exist.

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist.
A is 5 x 3, and B is 3 x 5.

Find the size of the product AB. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The size of product AB is .
B. The product AB does not exist.

Transcript text: The sizes of two matrices $A$ and $B$ are given. Find the sizes of the product $A B$ and the product $B A$, whenever these products exist. $A$ is $5 \times 3$, and $B$ is $3 \times 5$. Find the size of the product AB. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The size of product $A B$ is $\square$ $\square$ $\square$. B. The product $A B$ does not exist.

Solution

Solution Steps

Step 1: Determine the existence of AB

The product $AB$ exists because the number of columns in $A$ ( $n=3$ ) is equal to the number of rows in $B$ ( $p=3$ ). Thus, the size of the product $AB$ is $m \times q = 5 \times 5 = (5, 5)$ .

Step 2: Determine the existence of BA

The product $BA$ exists because the number of columns in $B$ ( $q=5$ ) is equal to the number of rows in $A$ ( $m=5$ ). Thus, the size of the product $BA$ is $p \times n = 3 \times 3 = (3, 3)$ .