Q18. - Algebra 2

Question

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

$A_{3\times 1}\cdot B_{1\times 5}$

Step-by-Step Solution

Answer

The required answer is that product is defined with dimensions$3\times 5$

Step 1- Determine the inner dimensions of both the matrices

The inner dimensions for both the provided matrices are represented by the number 1. 

Step 2 – Determine whether the product is defined or not

As the inner dimensions of provided matrices are the same which means that the product for the provided matrices is defined. 

Step 3- Write the dimensions that defines the product

As the numbers 3 and 5 represents the dimension that is outer so the multiplication between them represents the dimension related to product that is $3\times 5$