线性代数向量证明题设α1,α2,α3,α4线性相关,但其中任意三个向量都线性无关,证明:必存在一组全不为零的数k1,k2,k3,k4,使得k1α1+k2α2+k3α3+k4α4=0
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![线性代数向量证明题设α1,α2,α3,α4线性相关,但其中任意三个向量都线性无关,证明:必存在一组全不为零的数k1,k2,k3,k4,使得k1α1+k2α2+k3α3+k4α4=0](/uploads/image/z/2653828-52-8.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%90%91%E9%87%8F%E8%AF%81%E6%98%8E%E9%A2%98%E8%AE%BE%CE%B11%2C%CE%B12%2C%CE%B13%2C%CE%B14%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%2C%E4%BD%86%E5%85%B6%E4%B8%AD%E4%BB%BB%E6%84%8F%E4%B8%89%E4%B8%AA%E5%90%91%E9%87%8F%E9%83%BD%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%2C%E8%AF%81%E6%98%8E%EF%BC%9A%E5%BF%85%E5%AD%98%E5%9C%A8%E4%B8%80%E7%BB%84%E5%85%A8%E4%B8%8D%E4%B8%BA%E9%9B%B6%E7%9A%84%E6%95%B0k1%2Ck2%2Ck3%2Ck4%2C%E4%BD%BF%E5%BE%97k1%CE%B11%2Bk2%CE%B12%2Bk3%CE%B13%2Bk4%CE%B14%3D0)
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