证明a1a2a3a5-a4线性无关?
I suppose: "向量组a1a2a3a5的秩为4"instead of: "向量组a1a2a3a4的秩为4" 向量组a1a2a3a5的秩为4 => a1,a2,a3,a5线性无关 a1a2a3a4线性相关=> a4=m1a1 m2a2 m3a3 k1a1 k2a2 k3a3 k4(a5-a4)=0k1a1 k2a2 k3a3 k4a5 - k4(m1a1 m2a2 m3a3)=0(k1-k4m1)a1 (k2-k4m2)a2 (k3-k4m3)a3 k4a5=0=> (k1-k4m1)=0 (1) and(k2-k4m2)=0 (2) and(k3-k4m3)=0 (3) an...全部
I suppose: "向量组a1a2a3a5的秩为4"instead of: "向量组a1a2a3a4的秩为4" 向量组a1a2a3a5的秩为4 => a1,a2,a3,a5线性无关 a1a2a3a4线性相关=> a4=m1a1 m2a2 m3a3 k1a1 k2a2 k3a3 k4(a5-a4)=0k1a1 k2a2 k3a3 k4a5 - k4(m1a1 m2a2 m3a3)=0(k1-k4m1)a1 (k2-k4m2)a2 (k3-k4m3)a3 k4a5=0=> (k1-k4m1)=0 (1) and(k2-k4m2)=0 (2) and(k3-k4m3)=0 (3) andk4=0 (4)then k3=k2=k1=0iea1,a2,a3,a5-a4线性无关。
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