四阶行列式a23的所有正号项 线性代数 习题：写出四阶行列式中所有包含元素a32且带正号的...
\u56db\u9636\u884c\u5217\u5f0f\u4e2d,\u5305\u542ba23a24\u4e14\u53d6\u6b63\u53f7\u7684\u9879\u4e3a?\u5728\u884c\u5217\u5f0f\u5c55\u5f00\u9879\u4e2d\uff0c\u4e0d\u53ef\u80fd\u540c\u4e00\u884c\u7684\u4e24\u4e2a\u5143\u7d20\u5728\u540c\u4e00\u4e2a\u9879\u4e2d\uff01\uff08\u540c\u4e00\u4e2a\u5c55\u5f00\u9879\u4e2d\u4e5f\u4e0d\u53ef\u80fd\u6709\u540c\u4e00\u5217\u7684\u4e24\u4e2a\u5143\u7d20\uff09\u8fd9\u53ef\u4ee5\u4ece\u3010\u884c\u5217\u5f0f\u5b9a\u4e49\u3011\u5f97\u51fa\u63a8\u8bba\u3002
\u4f60\u7ed9\u51fa\u7684\u90a3\u4e24\u4e2a\u5143\u7d20\u6709\u9519\u8bef\u3002\u4f60\u53ef\u4ee5\u8865\u5145\u95ee\u9898\uff0c\u518d\u5f81\u7b54\u3002
\u4e3a\u4e86\u8868\u793a\u6211\u786e\u5b9e\u80fd\u505a\u8fd9\u6837\u7684\u9898\uff0c\u5047\u5b9a a24 \u662fa34\u5427\u3002\uff08\u6216\u8005 a42 \u4e5f\u662f\u53ef\u4ee5\u505a\u7684\uff09
\u542b a23a34 \u7684\u5c55\u5f00\u9879\u6709 a23a34a11a42 \u548c a23a34a12a41 \u4e24\u9879 \uff08\u6ca1\u6709\u522b\u7684\u9879\u4e86\uff0c\u4f60\u82e5\u5b58\u7591\uff0c\u5b8c\u5168\u53ef\u4ee5\u8ffd\u95ee\u3002\uff09
\u5bf9\u8fd9\u4e24\u9879\u5206\u522b\u8003\u67e5\u3010\u9006\u5e8f\u6570\u3011(\u7684\u5947\u5076\u6027\uff09
t(a23a34a11a42)=t(a11a23a34a42)=0+1+1+0=2 (\u4e3a\u5076\uff09
t(a23a34a12a41)=t(a12a23a34a41)=1+1+1+0=3 (\u4e3a\u5947\uff09
\u2234\u56db\u9636\u884c\u5217\u5f0f\u4e2d,\u5305\u542ba23a34\u4e14\u53d6\u6b63\u53f7\u7684\u9879\u4e3a a11a23a34a42
\u8bbe\u5305\u542ba32\u7684\u9879\u662fa1ia2ja32a4k\uff0c\u8fd9\u4e00\u9879\u5e26\u6b63\u53f7\uff0c\u5219\u6392\u5217ij2k\u7684\u9006\u5e8f\u6570\u662f\u5076\u6570\u3002ijk\u7684\u53d6\u503c\u4e00\u5171\u5c316\u79cd\u5f62\u5f0f\uff0c\u901a\u8fc7\u8ba1\u7b97\u9006\u5e8f\u6570\u5f97\uff1a4321\u30011423\u30013124\u7684\u9006\u5e8f\u6570\u662f\u5076\u6570\u3002\u6240\u4ee5\u56db\u9636\u884c\u5217\u5f0f\u4e2d\u5305\u542b\u5143\u7d20a32\u4e14\u5e26\u6b63\u53f7\u7684\u9879\u662f\uff1aa14a23a32a41\uff0ca11a24a32a43\uff0ca13a21a32a44
\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d\uff0d
2.2\uff1a\u505a\u6cd5\u53ef\u4ee5\uff0c\u5e72\u561b\u505a\u4e24\u904d\u5462\uff0c\u6309\u7167\u884c\u6807\u6392\u5e8f\u548c\u5217\u6807\u6392\u5e8f\u4e0d\u662f\u4e00\u56de\u4e8b\u561b\u3002
-a11a23a32a44 【N(1324)=1】
a11a23a34a42 【N(1342)=2】
-a12a23a34a41 【N(2341)=3】
a12a23a31a44 【N(2314)=2 】
a14a23a32a41 【N(4321)=6】
-a14a23a31a42 【N(4312)=5 】
所以，含a23的所有正号项为：a11a23a34a42、a12a23a31a44、a14a23a32a41 。
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