To find the determinant of the given [tex]\(2 \times 2\)[/tex] matrix:
[tex]\[
\begin{pmatrix}
11 & -10 \\
12 & 6
\end{pmatrix}
\][/tex]
we can use the formula for the determinant of a 2x2 matrix [tex]\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)[/tex], which is given by:
[tex]\[
\text{Determinant} = ad - bc
\][/tex]
For our specific matrix:
[tex]\[
a = 11, \quad b = -10, \quad c = 12, \quad d = 6
\][/tex]
Substitute the values into the formula:
[tex]\[
\text{Determinant} = (11 \cdot 6) - (-10 \cdot 12)
\][/tex]
Simplify the multiplication inside the expression:
[tex]\[
\text{Determinant} = (66) - (-120)
\][/tex]
Since subtracting a negative is the same as adding its absolute value:
[tex]\[
\text{Determinant} = 66 + 120
\][/tex]
Add the two terms:
[tex]\[
\text{Determinant} = 186
\][/tex]
Thus, the determinant of the matrix is:
[tex]\[
186
\][/tex]
