一道关于系数矩阵和增广矩阵解的问题，不理解下面这个说法。如果增广矩阵每行都有主元，那不是必定有解吗 为什么方程组有解无解要看系数矩阵的秩和增广矩阵的秩之间的关系
\u589e\u5e7f\u77e9\u9635\u4e0e\u7cfb\u6570\u77e9\u9635\u7528\u77e9\u9635\u6765\u89e3\u91ca\uff0c\u5199\u51fa\u589e\u5e7f\u77e9\u9635\u5e76\u53d8\u6362\u4e3a\u884c\u6700\u7b80\u77e9\u9635\u540e \u7cfb\u6570\u9635\u79e9\u82e5\u5c0f\u4e8e\u589e\u5e7f\u79e9\u4f1a\u51fa\u73b00=\u5e38\u6570\u7684\u60c5\u51b5\uff0c\u8fd9\u65f6\u65b9\u7a0b\u7ec4\u65e0\u89e3\u3002\u6709\u89e3\u5fc5\u987b\u79e9\u76f8\u7b49\u3002\u800c\u4e14\u4f60\u662f\u5148\u63a5\u89e6\u79e9\u7684\u6982\u5ff5\uff0c\u7136\u540e\u7528\u79e9\u6765\u89e3\u91ca\u65b9\u7a0b\u7ec4\u89e3\u7684\u60c5\u51b5\u5f88\u81ea\u7136\u3002
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\u6269\u5c55\u8d44\u6599\uff1a
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\u5f53r(A)<=n-2\u65f6\uff0c\u6700\u9ad8\u9636\u975e\u96f6\u5b50\u5f0f\u7684\u9636\u6570<=n-2\uff0c\u4efb\u4f55n-1\u9636\u5b50\u5f0f\u5747\u4e3a\u96f6\uff0c\u800c\u4f34\u968f\u9635\u4e2d\u7684\u5404\u5143\u7d20\u5c31\u662fn-1\u9636\u5b50\u5f0f\u518d\u52a0\u4e0a\u4e2a\u6b63\u8d1f\u53f7\uff0c\u6240\u4ee5\u4f34\u968f\u9635\u4e3a0\u77e9\u9635\u3002
\u5f53r(A)<=n-1\u65f6\uff0c\u6700\u9ad8\u9636\u975e\u96f6\u5b50\u5f0f\u7684\u9636\u6570<=n-1\uff0c\u6240\u4ee5n-1\u9636\u5b50\u5f0f\u6709\u53ef\u80fd\u4e0d\u4e3a\u96f6\uff0c\u6240\u4ee5\u4f34\u968f\u9635\u6709\u53ef\u80fd\u975e\u96f6\uff08\u7b49\u53f7\u6210\u7acb\u65f6\u4f34\u968f\u9635\u5fc5\u4e3a\u975e\u96f6\uff09\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u589e\u5e7f\u77e9\u9635
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u77e9\u9635\u7684\u79e9
此时 r(A) = m
<=> A 的列向量的秩为m
<=> A的列可生成R^m
<=> R^m 中向量可由A的列向量线性表示
<=> Ax=b (属于R^m) 有解
" 若 增广矩阵[A,b]每行都有主元, 则有解无解两种情况 "
最后一行的主元若在最后一列, 则无解, 否则有解
你先把定理看几遍，整个定理里没有涉及过增广矩阵
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