To determine the order of the matrix [tex]\( A + B \)[/tex], let's first understand the given matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
Matrix [tex]\( A \)[/tex]:
[tex]\[
A = \left[\begin{array}{c}
-9 \\
0 \\
3 \\
-1
\end{array}\right]
\][/tex]
Matrix [tex]\( B \)[/tex]:
[tex]\[
B = \left[\begin{array}{c}
0 \\
4 \\
-6 \\
2
\end{array}\right]
\][/tex]
These are both column vectors with 4 elements each.
When we add two matrices, the result will also be a matrix of the same order if they conform to the addition rule, which they do in this case. Therefore, the resulting matrix [tex]\( A + B \)[/tex] retains the same order as the individual matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
The resultant matrix [tex]\( A + B \)[/tex] will be:
[tex]\[
A + B = \left[\begin{array}{c}
-9 + 0 \\
0 + 4 \\
3 + (-6) \\
-1 + 2
\end{array}\right]
= \left[\begin{array}{c}
-9 \\
4 \\
-3 \\
1
\end{array}\right]
\][/tex]
Since [tex]\( A + B \)[/tex] is also a column vector with 4 elements, the order of the matrix [tex]\( A + B \)[/tex] is [tex]\( 4 \times 1 \)[/tex].
Thus, the correct answer is:
[tex]\[
\text{The order of matrix } A + B \text{ is } 4 \times 1
\][/tex]
