Question

Вычислить определитель.

Answer 1

$1)\; \left|\begin{array}{rrr}3&-2&1\\1&3&-2\\-1&2&-1\end{array}\right|=3\cdot \left|\begin{array}{rr}3&-2\\2&-1\end{array}\right|+2\cdot \left|\begin{array}{rr}1&-2\\-1&-1\end{array}\right|+ 1\cdot \left|\begin{array}{rr}1&3\\-1&2\end{array}\right|=\\\\\\=3\cdot (-3+4)+2\cdot (-1-2)+(2+3)=3-6+5=2$

$2)\; \left|\begin{array}{rrrr}1&1&1&1\\1&2&1&1\\1&1&3&1\\1&1&1&4\end{array}\right|=\; \Big [\; 2str-1str\; ;\; 3str-1str\; ;\; 4str-1str\; \Big ]=\\\\\\=\left|\begin{array}{rrrr}1&1&1&1\\0&1&0&0\\0&0&2&0\\0&0&0&3\end{array}\right|=\Big [\; raskruvaem\; \; po\; 1\; stolbcy\; \Big ]=1\cdot \left|\begin{array}{rrr}1&0&0\\0&2&0\\0&0&3\end{array}\right|=\\\\\\=\Big [\; raskruvaem\; \; po\; 1\; stolbcy\; \Big ]=1\cdot \left|\begin{array}{rr}2&0\\0&3\end{array}\right|=2\cdot 3=6$