To find the difference of two matrices, you subtract the corresponding elements of the matrices. Given the matrices:
[tex]\[
A = \left[\begin{array}{cc}
-4 & 8 \\
3 & 12
\end{array}\right]
\][/tex]
and
[tex]\[
B = \left[\begin{array}{cc}
2 & 1 \\
-14 & 15
\end{array}\right]
\][/tex]
we find the difference [tex]\( A - B \)[/tex]:
To find the element in the first row and first column of the resulting matrix, subtract the element in the first row and first column of [tex]\( B \)[/tex] from the element in the first row and first column of [tex]\( A \)[/tex]:
[tex]\[
-4 - 2 = -6
\][/tex]
To find the element in the first row and second column of the resulting matrix, subtract the element in the first row and second column of [tex]\( B \)[/tex] from the element in the first row and second column of [tex]\( A \)[/tex]:
[tex]\[
8 - 1 = 7
\][/tex]
To find the element in the second row and first column of the resulting matrix, subtract the element in the second row and first column of [tex]\( B \)[/tex] from the element in the second row and first column of [tex]\( A \)[/tex]:
[tex]\[
3 - (-14) = 3 + 14 = 17
\][/tex]
To find the element in the second row and second column of the resulting matrix, subtract the element in the second row and second column of [tex]\( B \)[/tex] from the element in the second row and second column of [tex]\( A \)[/tex]:
[tex]\[
12 - 15 = -3
\][/tex]
So, the difference of the matrices is:
[tex]\[
\left[\begin{array}{cc}
-6 & 7 \\
17 & -3
\end{array}\right]
\][/tex]
Thus, the correct answer is:
[tex]\[
\left[\begin{array}{cc}
-6 & 7 \\
17 & -3
\end{array}\right]
\][/tex]
