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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].
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].
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