QuestionEvaluate the determinant. $$\left|\begin{array}{rr} \frac{2}{3} & \frac{1}{3} \\ \frac{5}{12} & -\frac{1}{6} \end{array}\right|$$

Studdy Solution
Find a common denominator to simplify the subtraction:
- Convert $-\frac{1}{9}$ to $-\frac{4}{36}$ (since $-\frac{1}{9} = -\frac{4}{36}$)
Now, subtract:
$$\text{Determinant} = -\frac{4}{36} - \frac{5}{36} = -\frac{9}{36} = -\frac{1}{4}$$
The determinant of the matrix is:
$$\boxed{-\frac{1}{4}}$$