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PrecalculusSuperchallengeSystems, Matrices, and Determinants

Systems, Matrices, and Determinants · Superchallenge problem

A 2×22\times2 matrix MM satisfies M[12]=[54]M\begin{bmatrix}1\\2\end{bmatrix}=\begin{bmatrix}5\\4\end{bmatrix} and M[3−1]=[15]M\begin{bmatrix}3\\-1\end{bmatrix}=\begin{bmatrix}1\\5\end{bmatrix}. Find det⁡M\det M.