已知：a1,a2,a3线性无关，b1=a1+a2,b2=a2-a3,b3=a1+2a3 证明：向量组b1 b2 b3线性无关

---

(b1,b2,b3)=(a1+a2,a2-a3,a1+2a3) = (a1,a2,a3)K
K=
1 0 1
1 1 0
0 -1 2
因为 |K| = 2-1 = 1 ≠ 0
所局慎孙以K可孝数逆桐链
所以 r (b1,b2,b3)=r(a1,a2,a3) = 3
故 b1 b2 b3线性无关

---