a1(3,a,0),a2(a,1,2),a3(1,-2,1),a4(2,-4,2)
因為a3和a4對應(yīng)成比例
所以
只要 a1,a2,a3線性無關(guān)即可
也即
| 3 a 0
a 1 2
1 -2 1|≠0即可
=| 3 a 0
a-2 5 0
1 -2 1|
=3×5-a(a-2)
=-a²+2a+15≠0
a²-2a-15≠0
(a+3)(a-5)≠0
即
a≠-3且a≠5.