To solve the given problem, we need to perform matrix subtraction. Matrix subtraction is done element-wise, that is, each element in the resulting matrix is obtained by subtracting the corresponding elements of the two matrices.
Let's denote the matrices involved in the subtraction as follows:
Matrix [tex]\(A\)[/tex]:
[tex]\[
\left[\begin{array}{cc}
-20 & 16 \\
4 & 0 \\
8 & -8
\end{array}\right]
\][/tex]
Matrix [tex]\(B\)[/tex]:
[tex]\[
\left[\begin{array}{cc}
-5 & 1 \\
-6 & 7 \\
0 & 11
\end{array}\right]
\][/tex]
Matrix [tex]\(C\)[/tex] (result):
[tex]\[
\left[\begin{array}{cc}
x & y \\
10 & -7 \\
9 & -17
\end{array}\right]
\][/tex]
The element-wise subtraction is given by:
[tex]\[
A - B = C
\][/tex]
We can find each element of matrix [tex]\(C\)[/tex] by subtracting the corresponding elements of matrix [tex]\(B\)[/tex] from matrix [tex]\(A\)[/tex].
Let's start with the element in the first row and first column:
[tex]\[
x = -20 - (-5)
\][/tex]
Simplify:
[tex]\[
x = -20 + 5 = -15
\][/tex]
Next, let's find the element in the first row and second column:
[tex]\[
y = 16 - 1
\][/tex]
Simplify:
[tex]\[
y = 16 - 1 = 15
\][/tex]
Now we have determined that [tex]\(x = -15\)[/tex] and [tex]\(y = 15\)[/tex].
Thus, the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are:
[tex]\[
\boxed{x = -15, y = 15}
\][/tex]
