Question

para as matrizes A e B, qual sera o determinante de A - B:
A= 1 2 -1
2 3 0
2 0 2
B= -1 0 1
3 2 0
0 1 1

Answer 1

$A = \left[\begin{array}{ccc}1&2&-1\\2&3&0\\2&0&2\end{array}\right] ; B = \left[\begin{array}{ccc}-1&0&1\\3&2&0\\0&1&1\end{array}\right] \\\\\\ A-B = \left[\begin{array}{ccc}1&2&-1\\2&3&0\\2&0&2\end{array}\right] - \left[\begin{array}{ccc}-1&0&1\\3&2&0\\0&1&1\end{array}\right]=\\\\\\=\left[\begin{array}{ccc}1-(-1)&2-0&-1-1\\2-3&3-2&0-0\\2-0&0-1&2-1\end{array}\right]=\left[\begin{array}{ccc}2&2&-2\\-1&1&0\\2&-1&1\end{array}\right]$

Portanto, o determinante se dará por:
$(2*1*1)-(2*0*(-1)) +(2*0*2)-(2*(-1)*1)+((-2)*(-1)*(-1))-((-2)*1*2) = 2 +2+4+2-2+4 = 12$

Então, $det(A-B) = 12$