Step 1 :The given matrix is \[\left[\begin{array}{r}-3 \ 7\end{array}\right]\]
Step 2 :The size of a matrix is determined by the number of rows and columns it has. In this case, the matrix has 2 rows and 1 column. Therefore, the size of the matrix is \(2 \times 1\).
Step 3 :This matrix is a column matrix because it has only one column.
Step 4 :The additive inverse of a matrix is obtained by changing the sign of each element in the matrix. Therefore, the additive inverse of the given matrix is \[\left[\begin{array}{r}3 \ -7\end{array}\right]\]
Step 5 :\(\boxed{\text{The size of the matrix is } 2 \times 1\text{. This is a column matrix. The additive inverse of the matrix is } \left[\begin{array}{r}3 \ -7\end{array}\right]}\)