Question

线性代数 线性无关 证明题？ 求助 ！！！高手

Let v1, v2 and v3 be vectors in a vector space V . Decide whether or not w1 = v1 + v2, w2 = v2 + v3 and w3 = v1 − v3 are linearly independent, giving reasons for your answer. 怎么证明？ 谢谢

Answer 1

w1,w2,w3线性相关，因为w1-w2-w3=0，即存在不全为0的实数k1,k2,k3使得k1w1+k2w2+k3w3=0
所以w1,w2,w3线性相关