Question

calcule o determinante abaixo, desenvolvendo-o pela 2° linha [1 1 0 1] [a b c d] [1 0 1 1] [0 1 1 1]

Answer 1

Resolvamos por Laplace:

$\left|\begin{array}{cccc}1&1&0&1\\a&b&c&d\\1&0&1&1\\0&1&1&1\end{array}\right| =\\\\\\-a \left|\begin{array}{ccc}1&0&1\\0&1&1\\1&1&1\end{array}\right| +b\left|\begin{array}{ccc}1&0&1\\1&1&1\\0&1&1\end{array}\right|-c\left|\begin{array}{ccc}1&1&1\\1&0&1\\0&1&1\end{array}\right|+d\left|\begin{array}{ccc}1&1&0\\1&0&1\\0&1&1\end{array}\right|=\\\\\\-a(-1)+b(1)-c(-1)+d(-2)=a+b+c-2d$