Q45. - Algebra 2

Question

If C is a $5\times 1$ matrix and D is a$3\times 5$ matrix, what are the dimensions of DC?

A. $5\times 5$

B. $3\times 1$

C. $1\times 3$

D. DC is not defined

Step-by-Step Solution

Answer

The required option is C.

Step 1- Determine the inner dimensions of both the matrices

The inner dimensions for both the provided matrices are represented by the numbers 5 and 5. 

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 product is defined the dimensions that defines matrix is $3\times 1$.