Find the determinant of the matrix $\left[\begin{array}{cc}2 & 3 \\ -2 & 1\end{array}\right]$.
Answer
Final Answer: The determinant of the matrix \(\left[\begin{array}{cc}2 & 3 \\ -2 & 1\end{array}\right]\) is \(\boxed{8}\).
Step 1 ：Find the determinant of the matrix \(\left[\begin{array}{cc}2 & 3 \\ -2 & 1\end{array}\right]\).
Step 2 ：The determinant of a 2x2 matrix \(\left[\begin{array}{cc}a & b \\ c & d\end{array}\right]\) is calculated as \(ad - bc\).
Step 3 ：In this case, we need to calculate the determinant of the matrix \(\left[\begin{array}{cc}2 & 3 \\ -2 & 1\end{array}\right]\), which would be \(2*1 - 3*(-2)\).
Step 4 ：The determinant calculated is approximately 8.
Step 5 ：Final Answer: The determinant of the matrix \(\left[\begin{array}{cc}2 & 3 \\ -2 & 1\end{array}\right]\) is \(\boxed{8}\).
