Fine the size of the following matrix and its additive inverse matrix. Identify if it is a square,

column, or row matrix:

[ 2 -3 7
1 0 4 ]

From the brackets, it is not clear if the "matrix" has one single row or two rows.

Brackets are usually used to delimit a row
If it has two rows, then you could write it as
2 -3 7
1 0 4
or
[2 -3 7]
[1 0 4]
If it has only one row, it would be written as
[2 -3 7 1 0 4]

In any case, an additive inverse is a matrix of the same "shape", i.e. containing the same number of rows and columns, that when added to the given matrix, results in zero.

In other words, the additive inverse of matrix A is -A.

For example,
The additive inverse of
[ 2 3 4]
is
[ -2 -3 -4 ]
because
[2 3 4]+[-2 -3 -4] = [0 0 0]

To find the size of a matrix, we count the number of rows and columns.

The given matrix: [ 2 -3 7
1 0 4 ]

The matrix has 2 rows and 3 columns.

Now, let's find the additive inverse matrix.

To find the additive inverse of a matrix, we need to negate each element. Negating a number means changing its sign to the opposite.

The given matrix: [ 2 -3 7
1 0 4 ]

The additive inverse matrix would be: [ -2 3 -7
-1 0 -4 ]

Now, let's identify the type of matrix.

Since the matrix has 2 rows and 3 columns, it is neither a square matrix (which has an equal number of rows and columns) nor a row matrix (which has only one row). Therefore, it can be identified as a column matrix.