Question

calcule o determinante da matriz 3x3 abaixo:
A= 2 3 1
1 2 4
0 5 1​

Answer 1

$\sf A=\left[\begin{array}{c c c}\sf2&\sf3&\sf1\\\sf1&\sf2&\sf4\\\sf0&\sf5&\sf1\end{array}\right]\begin{array}{c c}\sf2&\sf3\\\sf1&\sf2\\\sf0&\sf5\end{array}$

$\sf d_p=2\cdot2\cdot1=4$

$\sf d_p=3\cdot4\cdot0=0$

$\sf d_p=1\cdot1\cdot5=5$

$\sf d_p=4+0+5$

$\sf d_p=9$

$\sf d_s=3\cdot1\cdot1=3$

$\sf d_s=2\cdot4\cdot5=40$

$\sf d_s=1\cdot2\cdot0=0$

$\sf d_s=3+40+0$

$\sf d_s=43$

$\sf det_A=d_p-d_s$

$\sf det_A=9-43$

$\red{\sf det_A=-34}$