To determine the order of the resulting matrix when adding matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we first need to understand the dimensions of the given matrices.
Matrix [tex]\( A \)[/tex] is:
[tex]\[
A = \begin{pmatrix}
-9 \\
0 \\
3 \\
-1
\end{pmatrix}
\][/tex]
This matrix has:
- 4 rows
- 1 column
Matrix [tex]\( B \)[/tex] is:
[tex]\[
B = \begin{pmatrix}
0 \\
4 \\
-6 \\
2
\end{pmatrix}
\][/tex]
This matrix also has:
- 4 rows
- 1 column
The addition of two matrices is only possible if they have the same dimensions. Since both [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have 4 rows and 1 column, their sum [tex]\( A + B \)[/tex] will also have the same number of rows and columns.
Therefore, the resulting matrix [tex]\( A + B \)[/tex] will have:
- 4 rows
- 1 column
Hence, the order of the matrix [tex]\( A + B \)[/tex] is [tex]\( \boxed{{4, 1}} \)[/tex].
