数学线性代数一道非常简单的证明题A是n阶方阵,B是nxs矩阵,且R(B)=n,证明:若AB=0,则A=0证1:B=(B1 B2 ...BS)列向量AB=(AB1 AB2 ...ABS)因为R(B)=n所以B1 B2 ...BS线性无关所以A=0证2:AB=0BTAT=0TBT=(
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![数学线性代数一道非常简单的证明题A是n阶方阵,B是nxs矩阵,且R(B)=n,证明:若AB=0,则A=0证1:B=(B1 B2 ...BS)列向量AB=(AB1 AB2 ...ABS)因为R(B)=n所以B1 B2 ...BS线性无关所以A=0证2:AB=0BTAT=0TBT=(](/uploads/image/z/8846738-26-8.jpg?t=%E6%95%B0%E5%AD%A6%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E4%B8%80%E9%81%93%E9%9D%9E%E5%B8%B8%E7%AE%80%E5%8D%95%E7%9A%84%E8%AF%81%E6%98%8E%E9%A2%98A%E6%98%AFn%E9%98%B6%E6%96%B9%E9%98%B5%2CB%E6%98%AFnxs%E7%9F%A9%E9%98%B5%2C%E4%B8%94R%EF%BC%88B%EF%BC%89%3Dn%2C%E8%AF%81%E6%98%8E%EF%BC%9A%E8%8B%A5AB%3D0%2C%E5%88%99A%3D0%E8%AF%811%EF%BC%9AB%3D%EF%BC%88B1+B2+...BS%EF%BC%89%E5%88%97%E5%90%91%E9%87%8FAB%3D%EF%BC%88AB1+AB2+...ABS%EF%BC%89%E5%9B%A0%E4%B8%BAR%EF%BC%88B%EF%BC%89%3Dn%E6%89%80%E4%BB%A5B1+B2+...BS%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%E6%89%80%E4%BB%A5A%3D0%E8%AF%812%EF%BC%9AAB%3D0BTAT%3D0TBT%3D%EF%BC%88)
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