[a1+a2,a2,a1+a2-a3] = [a1,a2,a3] K
K=
1 0 1
1 1 1
0 0 -1
|K| = -1.
所以 |[a1+a2,a2,a1+a2-a3]| = |A||K| = 2*(-1) = -2.