Question

calcule os seguintes determinantes:​

Answer 1

Resposta:

a) Det = 22    c) Det = (-1)

b) Det = 2      d) Det = 15

Explicação passo a passo:

$a)\ \ \left[\begin{array}{ccc}3&2&1\\1&2&5\\1&-1&0\end{array}\right] \\\\\\Det=3\times2\times0\ +\ 2\times5\times1\ +\ 1\times1\times(-1)\ -\ 1\times2\times1 - (-1)\times5\times3\ -\ 0\times1\times2 \\\\Det=0\ +\ 10\ +\ (-1)\ -\ 2 - (-15)\ -\ 0 \\\\Det=10\ -\ 1\ -\ 2\ +\ 15 \\\\Det=7\ +\ 15 \\\\Det=22$

$b)\ \ \left[\begin{array}{ccc}1&-1&2\\5&7&-4\\1&0&1\end{array}\right] \\\\\\Det=1\times7\times1\ +\ (-1)\times(-4)\times1\ +\ 2\times5\times0\ -\ 1\times7\times2 - 0\times(-4)\times1\ -\ 1\times5\times(-1) \\\\Det=7+4+0-14-0-(-5) \\\\Det=7+4-14+5\\\\Det=11-9\\\\Det=2$

$c)\ \ \left[\begin{array}{ccc}0&1&3\\-4&2&5\\-3&0&-1\end{array}\right] \\\\\\Det=0\times2\times(-1)\ +\ 1\times5\times(-3)\ +\ 3\times(-4)\times0\ -\ (-3)\times2\times3 - 0\times5\times0\ -\ (-1)\times(-4)\times1 \\\\Det=0+(-15)+0-(-18)-0-4\\\\Det=(-15)+18-4\\\\Det=3-4\\\\Det=(-1)$

$d)\ \ \left[\begin{array}{ccc}1&2&4\\0&3&9\\0&0&5\end{array}\right] \\\\\\Det=1\times3\times5\ +\ 2\times9\times0\ +\ 4\times0\times0\ -\ 0\times3\times4 - 0\times9\times1\ -\ 5\times0\times2 \\\\Det=15+0+0-0-0-0\\\\Det=15$