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Sagot :
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]
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]
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