Answer :
To solve for the matrix [tex]\( X \)[/tex] such that [tex]\( B - X = A \)[/tex], we rearrange the equation to solve for [tex]\( X \)[/tex]:
[tex]\[ X = B - A \][/tex]
Given the matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[ A = \begin{pmatrix} -1 & -2 & 3 \\ 4 & 8 & -6 \\ 0 & 1 & 5 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} -5 & -1 & 6 \\ 4 & 1 & 2 \\ 0 & -3 & 2 \end{pmatrix} \][/tex]
We perform the matrix subtraction element-wise:
[tex]\[ X = B - A \][/tex]
[tex]\[ X = \begin{pmatrix} -5 & -1 & 6 \\ 4 & 1 & 2 \\ 0 & -3 & 2 \end{pmatrix} - \begin{pmatrix} -1 & -2 & 3 \\ 4 & 8 & -6 \\ 0 & 1 & 5 \end{pmatrix} \][/tex]
Now, subtract each corresponding element:
For the first row:
[tex]\[ \begin{pmatrix} -5 - (-1) & -1 - (-2) & 6 - 3 \end{pmatrix} = \begin{pmatrix} -4 & 1 & 3 \end{pmatrix} \][/tex]
For the second row:
[tex]\[ \begin{pmatrix} 4 - 4 & 1 - 8 & 2 - (-6) \end{pmatrix} = \begin{pmatrix} 0 & -7 & 8 \end{pmatrix} \][/tex]
For the third row:
[tex]\[ \begin{pmatrix} 0 - 0 & -3 - 1 & 2 - 5 \end{pmatrix} = \begin{pmatrix} 0 & -4 & -3 \end{pmatrix} \][/tex]
Combining these results, we get the matrix [tex]\( X \)[/tex]:
[tex]\[ X = \begin{pmatrix} -4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3 \end{pmatrix} \][/tex]
Therefore, the correct option is:
[tex]\[ \begin{pmatrix} -4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3 \end{pmatrix} \][/tex]
So, the correct answer is:
[tex]\[ \left[\begin{array}{ccc}-4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3\end{array}\right] \][/tex]
[tex]\[ X = B - A \][/tex]
Given the matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[ A = \begin{pmatrix} -1 & -2 & 3 \\ 4 & 8 & -6 \\ 0 & 1 & 5 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} -5 & -1 & 6 \\ 4 & 1 & 2 \\ 0 & -3 & 2 \end{pmatrix} \][/tex]
We perform the matrix subtraction element-wise:
[tex]\[ X = B - A \][/tex]
[tex]\[ X = \begin{pmatrix} -5 & -1 & 6 \\ 4 & 1 & 2 \\ 0 & -3 & 2 \end{pmatrix} - \begin{pmatrix} -1 & -2 & 3 \\ 4 & 8 & -6 \\ 0 & 1 & 5 \end{pmatrix} \][/tex]
Now, subtract each corresponding element:
For the first row:
[tex]\[ \begin{pmatrix} -5 - (-1) & -1 - (-2) & 6 - 3 \end{pmatrix} = \begin{pmatrix} -4 & 1 & 3 \end{pmatrix} \][/tex]
For the second row:
[tex]\[ \begin{pmatrix} 4 - 4 & 1 - 8 & 2 - (-6) \end{pmatrix} = \begin{pmatrix} 0 & -7 & 8 \end{pmatrix} \][/tex]
For the third row:
[tex]\[ \begin{pmatrix} 0 - 0 & -3 - 1 & 2 - 5 \end{pmatrix} = \begin{pmatrix} 0 & -4 & -3 \end{pmatrix} \][/tex]
Combining these results, we get the matrix [tex]\( X \)[/tex]:
[tex]\[ X = \begin{pmatrix} -4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3 \end{pmatrix} \][/tex]
Therefore, the correct option is:
[tex]\[ \begin{pmatrix} -4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3 \end{pmatrix} \][/tex]
So, the correct answer is:
[tex]\[ \left[\begin{array}{ccc}-4 & 1 & 3 \\ 0 & -7 & 8 \\ 0 & -4 & -3\end{array}\right] \][/tex]
