线性代数高手进.设 a1=1 ,a2= 2 ,a3=1 ,b=11 2 -1 02 1 4 32 3 0 1证明向量b可

(a1,a2,a3,b) =
1 2 1 1
1 2 -1 0
2 1 4 3
2 3 0 1
r2-r1,r3-2r1,r4-2r1
1 2 1 1
0 0 -2 -1
0 -3 2 1
0 -1 -2 -1
r3+r2,r4-r2
1 2 1 1
0 0 -2 -1
0 -3 0 0
0 -1 0 0
r1+2r4,r3-3r4,r4*(-1),r2*(-1/2), r1-r2
1 0 0 1/2
0 0 1 1/2
0 0 0 0
0 1 0 0
b = (1/2)a1 + 0a2 + (1/2)a3.