Sure, let's find the difference between the two matrices by subtracting corresponding elements step-by-step.
We are given two matrices:
Matrix [tex]\( A \)[/tex]:
[tex]\[
\begin{pmatrix}
-11 & 4 \\
3 & -2 \\
-10 & 13
\end{pmatrix}
\][/tex]
Matrix [tex]\( B \)[/tex]:
[tex]\[
\begin{pmatrix}
1 & 2 \\
1 & 3 \\
-2 & 6
\end{pmatrix}
\][/tex]
To find the difference [tex]\( A - B \)[/tex], we subtract each element of matrix [tex]\( B \)[/tex] from the corresponding element of matrix [tex]\( A \)[/tex].
Let's perform the subtraction element by element:
First row:
[tex]\[
\begin{pmatrix}
-11 - 1 & 4 - 2
\end{pmatrix}
=
\begin{pmatrix}
-12 & 2
\end{pmatrix}
\][/tex]
Second row:
[tex]\[
\begin{pmatrix}
3 - 1 & -2 - 3
\end{pmatrix}
=
\begin{pmatrix}
2 & -5
\end{pmatrix}
\][/tex]
Third row:
[tex]\[
\begin{pmatrix}
-10 - (-2) & 13 - 6
\end{pmatrix}
=
\begin{pmatrix}
-8 & 7
\end{pmatrix}
\][/tex]
Combining all the rows together, the difference matrix [tex]\( A - B \)[/tex] is:
[tex]\[
\begin{pmatrix}
-12 & 2 \\
2 & -5 \\
-8 & 7
\end{pmatrix}
\][/tex]
Thus, the result of the subtraction is:
[tex]\[
\begin{pmatrix}
-12 & 2 \\
2 & -5 \\
-8 & 7
\end{pmatrix}
\][/tex]
