Question

Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be two matrices of the same order \[m\times n\]. If \[C=A+B=[c_{ij}]\], which entry rule defines \[C\]?

Options

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

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

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

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

Answer 1

The sum \[C=A+B\] is formed by adding corresponding entries of \[A\] and \[B\]. Thus every entry is \[c_{ij}=a_{ij}+b_{ij}\].