解: (a1,a2,a3,a4,a) =
1 -1 3 -2 4
1 -3 2 -6 1
1 5 -1 10 6
3 1 p+2 p 10
r3-r1-r2-r3, r3-r2,r2-r1
1 -1 3 -2 4
0 -2 -1 -4 -3
0 8 -3 16 5
0 0 p-2 p-2 -1
r3+4r2
1 -1 3 -2 4
0 -2 -1 -4 -3
0 0 -7 0 -7
0 0 p-2 p-2 -1
r3*(-1/7),r1-3r3,r2+r3,r4-(p-1)r3
1 -1 0 -2 1
0 -2 0 -4 -2
0 0 1 0 1
0 0 0 p-2 -p+1
r2*(-1/2),r1+r2
1 0 0 0 2
0 1 0 2 1
0 0 1 0 1
0 0 0 p-2 -p+1
当p=2时, a1,a2,a3,a4线性相关, r(a1,a2,a3,a4)=3, a1,a2,a3 是一个极大无关组.
当p≠2时, a1,a2,a3,a4线性无关.
此时, (a1,a2,a3,a4,a) -->...
r4*[1/(p-2)], r2-2r4
1 0 0 0 2
0 1 0 0 (3p-4)/(p-2)
0 0 1 0 1
0 0 0 1 -(p-1)/(p-2)
a=2a1+[(3p-4)/(p-2)]a2+a3-[(p-1)/(p-2)]a4.