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Find the determinancof the matrix Q.

Find the determinancof the matrix Q.-example-1
User Boston
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Using a Laplace expansion along the first column, we have


\det Q=2\det\begin{bmatrix}2&1\\-1&6\end{bmatrix}+3\det\begin{bmatrix}3&4\\-1&6\end{bmatrix}+5\det\begin{bmatrix}3&4\\2&1\end{bmatrix}

The determinant of a 2x2 matrix is trivial,


\det\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc

So we have


\det Q=2\cdot13+3\cdot22+5\cdot(-5)=67

User Vibha Rathi
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