Question

Let \[A=[a_{ij}]_{m\times n}\] be a matrix and \[k\] be a real number (scalar). Which expression defines the scalar multiple of \[A\] by \[k\]?

Options

• \[kA=[a_{ij}]_{k\times n}\]

• \[kA=[ka_{ij}]_{m\times n}\]

• \[kA=[ka_{ij}]_{n\times m}\]

• \[kA=[a_{ij}+k]_{m\times n}\]

Answer 1

The scalar multiple is obtained by multiplying each entry \[a_{ij}\] by \[k\]. Therefore, the resulting matrix is \[kA=[ka_{ij}]_{m\times n}\].