To perform the matrix subtraction, we subtract each corresponding element of Matrix [tex]\( B \)[/tex] from Matrix [tex]\( A \)[/tex]. Here are the given matrices:
[tex]\[
A = \left[\begin{array}{rr}
0 & 0 \\
-8 & 1
\end{array}\right]
\][/tex]
[tex]\[
B = \left[\begin{array}{rr}
7 & 3 \\
-3 & 1
\end{array}\right]
\][/tex]
We will calculate the element-wise subtraction step by step.
1. Subtract the element in the first row, first column of [tex]\( B \)[/tex] from the element in the first row, first column of [tex]\( A \)[/tex]:
[tex]\[
0 - 7 = -7
\][/tex]
2. Subtract the element in the first row, second column of [tex]\( B \)[/tex] from the element in the first row, second column of [tex]\( A \)[/tex]:
[tex]\[
0 - 3 = -3
\][/tex]
3. Subtract the element in the second row, first column of [tex]\( B \)[/tex] from the element in the second row, first column of [tex]\( A \)[/tex]:
[tex]\[
-8 - (-3) = -8 + 3 = -5
\][/tex]
4. Subtract the element in the second row, second column of [tex]\( B \)[/tex] from the element in the second row, second column of [tex]\( A \)[/tex]:
[tex]\[
1 - 1 = 0
\][/tex]
Combining these results, we get the resulting matrix:
[tex]\[
A - B = \left[\begin{array}{rr}
-7 & -3 \\
-5 & 0
\end{array}\right]
\][/tex]
Therefore, the correct choice is:
A.
[tex]\[
\left[\begin{array}{rr}
0 & 0 \\
-8 & 1
\end{array}\right]-\left[\begin{array}{rr}
7 & 3 \\
-3 & 1
\end{array}\right]=
\left[\begin{array}{rr}
-7 & -3 \\
-5 & 0
\end{array}\right]
\][/tex]
