Question 6.2.6: Use Laplace expansion to compute det A for A=[1 0 1 2 9 1 3 ......

Looking for rows or columns with as many zeros as possible, we choose the second column:

\det A = −a_{12} \det (A_{12}) + a_{22} \det (A_{22}) − a_{32} \det (A_{32}) + a_{42} \det (A_{42})

=\det \begin{bmatrix}1&1&2\\9&2&0\\5&0&3\end{bmatrix}-2\det\begin{bmatrix}1&1&2\\9&2&0\\5&0&3\end{bmatrix}

= −20 − 21 − 2(−30 − 18) = 55.