To determine the order of the matrix resulting from the addition of [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we need to follow these steps:
1. Identify the order of matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- Matrix [tex]\( A \)[/tex] is given as:
[tex]\[
A = \begin{bmatrix}
-9 \\
0 \\
3 \\
-1
\end{bmatrix}
\][/tex]
Matrix [tex]\( A \)[/tex] has 4 rows and 1 column. Therefore, the order of matrix [tex]\( A \)[/tex] is [tex]\( 4 \times 1 \)[/tex].
- Matrix [tex]\( B \)[/tex] is given as:
[tex]\[
B = \begin{bmatrix}
0 \\
4 \\
-6 \\
2
\end{bmatrix}
\][/tex]
Matrix [tex]\( B \)[/tex] also has 4 rows and 1 column. Therefore, the order of matrix [tex]\( B \)[/tex] is [tex]\( 4 \times 1 \)[/tex].
2. Add matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
Since both matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex] have the same order ([tex]\( 4 \times 1 \)[/tex]), we can add them element-wise to get the resulting matrix [tex]\( C \)[/tex]:
[tex]\[
A + B = \begin{bmatrix}
-9 + 0 \\
0 + 4 \\
3 + -6 \\
-1 + 2
\end{bmatrix}
= \begin{bmatrix}
-9 \\
4 \\
-3 \\
1
\end{bmatrix}
\][/tex]
3. Determine the order of the resulting matrix [tex]\( C \)[/tex]:
The matrix [tex]\( C \)[/tex] resulting from the addition of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] has the same number of rows and columns as the original matrices. Therefore, it has 4 rows and 1 column.
Thus, the order of the matrix [tex]\( A + B \)[/tex] is [tex]\( 4 \times 1 \)[/tex].
To complete the question, select the correct answer from the drop-down menu:
The order of matrix [tex]\( A+B \)[/tex] is [tex]\( 4 \times 1 \)[/tex].
