Question

Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be matrices of the same order \[m\times n\]. If \[D=A-B=[d_{ij}]\], which rule defines \[D\]?

Options

• \[d_{ij}=a_{ij}+b_{ij}\text{ for all }i,j\]

• \[d_{ij}=a_{ij}-b_{ij}\text{ for all }i,j\]

• \[d_{ij}=b_{ij}-a_{ij}\text{ for all }i,j\]

• \[d_{ij}=a_{ji}-b_{ji}\text{ for all }i,j\]

Answer 1

The difference \[D=A-B\] is obtained by subtracting corresponding entries. Hence \[d_{ij}=a_{ij}-b_{ij}\] for all \[i,j\].