To solve for the matrix [tex]\(A - B\)[/tex], we need to subtract each corresponding element of matrix [tex]\(B\)[/tex] from matrix [tex]\(A\)[/tex].
Given the matrices:
[tex]\[ A = \begin{bmatrix}
3 & -7 \\
6 & 1 \\
-8 & 5
\end{bmatrix} \][/tex]
[tex]\[ B = \begin{bmatrix}
1 & -1 \\
0 & 8 \\
-5 & 3
\end{bmatrix} \][/tex]
We subtract each element in [tex]\(B\)[/tex] from the corresponding element in [tex]\(A\)[/tex] as follows:
1. For the first row and first column element:
[tex]\[ 3 - 1 = 2 \][/tex]
2. For the first row and second column element:
[tex]\[ -7 - (-1) = -7 + 1 = -6 \][/tex]
3. For the second row and first column element:
[tex]\[ 6 - 0 = 6 \][/tex]
4. For the second row and second column element:
[tex]\[ 1 - 8 = -7 \][/tex]
5. For the third row and first column element:
[tex]\[ -8 - (-5) = -8 + 5 = -3 \][/tex]
6. For the third row and second column element:
[tex]\[ 5 - 3 = 2 \][/tex]
Combining all the results, the resulting matrix [tex]\(A - B\)[/tex] is:
[tex]\[ \begin{bmatrix}
2 & -6 \\
6 & -7 \\
-3 & 2
\end{bmatrix} \][/tex]
Thus, the correct answer is:
[tex]\[
C. \begin{bmatrix}
-1 & -6 \\
6 & -7 \\
-3 & 2
\end{bmatrix}
\][/tex]
Now we choose the option matching this matrix:
[tex]\[
C. \left[\begin{array}{cc}-1 & -6 \\ 6 & -7 \\ -3 & 2\end{array}\right]
\][/tex]
