Answer:
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Step-by-step explanation:
To find the determinant of a 2x2 matrix:
\[ \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \]
Given the matrix:
\[ \begin{vmatrix} -24 & -3 \\ 3 & 45 \end{vmatrix} \]
We can apply the formula:
\[ \text{Determinant} = (-24)(45) - (-3)(3) \]
\[ \text{Determinant} = -1080 - (-9) \]
\[ \text{Determinant} = -1080 + 9 \]
\[ \text{Determinant} = -1071 \]
So, the determinant of the given matrix is \( -1071 \).
