{"id":28893,"date":"2025-11-28T22:02:23","date_gmt":"2025-11-28T13:02:23","guid":{"rendered":"https:\/\/lanqiu.aboutphlaw.com\/?p=28893"},"modified":"2025-11-28T22:02:23","modified_gmt":"2025-11-28T13:02:23","slug":"3x3-inverse-matrix-calculation-methods-and-applications-2","status":"publish","type":"post","link":"https:\/\/lanqiu.aboutphlaw.com\/3x3\/3x3-inverse-matrix-calculation-methods-and-applications-2","title":{"rendered":"3&#215;3 \u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3068\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\uff08\u6570\u5b66\u306e\u57fa\u790e\u304b\u3089\u5fdc\u7528\u307e\u3067\u3092\u7db2\u7f85\u3057\u305f\u7279\u96c6\uff09"},"content":{"rendered":"<h4>\u76ee\u5f551<\/h4>\n<p>3&#215;3 \u9006\u884c\u5217\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7fa9\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u884c\u5217\u3068\u306f\u3001\u6570\u5024\u3084\u5909\u6570\u3092\u884c\u3068\u5217\u306b\u4e26\u3079\u305f\u3082\u306e\u3067\u3042\u308a\u30013&#215;3 \u306e\u884c\u5217\u306f3\u3064\u306e\u884c\u30683\u3064\u306e\u5217\u304b\u3089\u6210\u308a\u307e\u3059\u3002\u9006\u884c\u5217\u3068\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u884c\u5217\u3068\u305d\u306e\u9006\u884c\u5217\u3092\u639b\u3051\u5408\u308f\u305b\u305f\u3068\u304d\u306b\u5358\u4f4d\u884c\u5217\u306b\u306a\u308b\u884c\u5217\u306e\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u884c\u5217 A \u306e\u9006\u884c\u5217 A<sup>-1<\/sup> \u306b\u5bfe\u3057\u3066\u3001A \u00d7 A<sup>-1<\/sup> = I \u3068\u3044\u3046\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u307e\u3059\u3002\u884c\u5217\u304c\u9006\u884c\u5217\u3092\u6301\u3064\u305f\u3081\u306e\u6761\u4ef6\u306f\u3001\u884c\u5217\u306e\u884c\u5217\u5f0f\u304c0\u3067\u306a\u3044\u3053\u3068\u3067\u3059\u30023&#215;3 \u306e\u884c\u5217\u306e\u9006\u884c\u5217\u3092\u6c42\u3081\u308b\u516c\u5f0f\u306b\u306f\u3001\u884c\u5217\u5f0f\u3084\u4f59\u56e0\u5b50\u3092\u7528\u3044\u308b\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h4>\u76ee\u5f552<\/h4>\n<p>3&#215;3 \u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u884c\u5217 A \u306e\u884c\u5217\u5f0f det(A) \u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u884c\u5217 A \u304c\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3068\u3057\u307e\u3059<\/p>\n<p>A = &nbsp;&nbsp;&nbsp;&nbsp;[a<sub>11<\/sub> a<sub>12<\/sub> a<sub>13<\/sub><br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<sub>21<\/sub> a<sub>22<\/sub> a<sub>23<\/sub><br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a<sub>31<\/sub> a<sub>32<\/sub> a<sub>33<\/sub>]<\/p>\n<p>\u3053\u306e\u884c\u5217\u306e\u884c\u5217\u5f0f\u306f\u3001det(A) = a<sub>11<\/sub>(a<sub>22<\/sub>a<sub>33<\/sub> &#8211; a<sub>23<\/sub>a<sub>32<\/sub>) &#8211; a<sub>12<\/sub>(a<sub>21<\/sub>a<sub>33<\/sub> &#8211; a<sub>23<\/sub>a<sub>31<\/sub>) + a<sub>13<\/sub>(a<sub>21<\/sub>a<sub>32<\/sub> &#8211; a<sub>22<\/sub>a<sub>31<\/sub>) \u3067\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u6b21\u306b\u3001\u4f59\u56e0\u5b50\u884c\u5217\u3092\u6c42\u3081\u3001\u305d\u308c\u3092\u8ee2\u7f6e\u3057\u305f\u3082\u306e\u304c\u4f34\u56e0\u5b50\u884c\u5217\u3067\u3059\u3002\u6700\u7d42\u7684\u306b\u3001\u9006\u884c\u5217 A<sup>-1<\/sup> \u306f\u3001(1\/det(A)) \u00d7 \u4f34\u56e0\u5b50\u884c\u5217\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<h4>\u76ee\u5f553<\/h4>\n<p>3&#215;3 \u9006\u884c\u5217\u306e\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u8ff0\u3079\u307e\u3059\u3002\u9006\u884c\u5217\u306f\u3001\u7279\u306b\u7dda\u5f62\u4ee3\u6570\u306e\u554f\u984c\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6c42\u3081\u308b\u969b\u3001\u884c\u5217\u5f62\u5f0f\u3067\u66f8\u304b\u308c\u305f\u65b9\u7a0b\u5f0f Ax = b \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001x \u306f A<sup>-1<\/sup>b \u306b\u3088\u308a\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u9006\u884c\u5217\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u52b9\u7387\u7684\u306b\u5c0e\u51fa\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u9006\u884c\u5217\u306f\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3084\u4fe1\u53f7\u51e6\u7406\u3001\u6a5f\u68b0\u5b66\u7fd2\u306e\u9818\u57df\u3067\u3082\u5229\u7528\u3055\u308c\u3001\u7279\u306b\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3084\u7dda\u5f62\u56de\u5e30\u5206\u6790\u306b\u304a\u3044\u3066\u591a\u304f\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>\u76ee\u5f554<\/h4>\n<p>3&#215;3 \u9006\u884c\u5217\u306e\u8a08\u7b97\u3068\u5fdc\u7528\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9\u3092\u6319\u3052\u307e\u3059\u3002\u307e\u305a\u3001\u9006\u884c\u5217\u3092\u6c42\u3081\u308b\u969b\u306b\u306f\u5e38\u306b\u884c\u5217\u306e\u884c\u5217\u5f0f\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u884c\u5217\u5f0f\u304c0\u306e\u5834\u5408\u3001\u9006\u884c\u5217\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u5927\u304d\u306a\u884c\u5217\u3092\u6271\u3046\u5834\u5408\u3001\u6570\u5024\u8a08\u7b97\u306e\u7cbe\u5ea6\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\u6570\u5024\u8a08\u7b97\u306b\u304a\u3044\u3066\u306f\u3001\u8aa4\u5dee\u3084\u6841\u843d\u3061\u304c\u767a\u751f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u8a08\u7b97\u7d50\u679c\u304c\u7406\u8ad6\u7684\u306a\u80cc\u666f\u3068\u4e00\u81f4\u3059\u308b\u304b\u78ba\u8a8d\u3059\u308b\u3053\u3068\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u9006\u884c\u5217\u306e\u5b58\u5728\u78ba\u8a8d\u3084\u8a08\u7b97\u65b9\u6cd5\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u7dda\u5f62\u4ee3\u6570\u306e\u69d8\u3005\u306a\u554f\u984c\u306b\u5bfe\u51e6\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h4>\u76ee\u5f555<\/h4>\n<p>\u6700\u5f8c\u306b\u30013&#215;3 \u9006\u884c\u5217\u306e\u5b9f\u969b\u306e\u8a08\u7b97\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002\u6b21\u306e\u884c\u5217 A \u3092\u8003\u3048\u307e\u3059<\/p>\n<p>A = [2 1 3<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;1 0 2<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;3 2 1]<\/p>\n<p>\u307e\u305a\u3001\u884c\u5217\u5f0f det(A) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u4f59\u56e0\u5b50\u884c\u5217\u3092\u6c42\u3081\u3001\u4f34\u56e0\u5b50\u884c\u5217\u3092\u5f97\u305f\u5f8c\u3001\u9006\u884c\u5217 A<sup>-1<\/sup> \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u901a\u3058\u3066\u30013&#215;3 \u306e\u9006\u884c\u5217\u8a08\u7b97\u306e\u5177\u4f53\u7684\u306a\u624b\u9806\u3068\u305d\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u6570\u5024\u3092\u901a\u3058\u3066\u7406\u89e3\u3092\u6df1\u3081\u308b\u3053\u3068\u304c\u3001\u9006\u884c\u5217\u306e\u8a08\u7b97\u80fd\u529b\u3092\u5411\u4e0a\u3055\u305b\u308b\u9375\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30bf\u30a4\u30c8\u30eb3&#215;3 \u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3068\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\uff08\u6570\u5b66\u306e\u57fa\u790e\u304b\u3089\u5fdc\u7528\u307e\u3067\u3092\u7db2\u7f85\u3057\u305f\u7279\u96c6\uff09<\/p>\n","protected":false},"author":1,"featured_media":1022,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[10531,6790,7468],"class_list":["post-28893","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3x3","tag-3x3","tag-6790","tag-7468"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>3x3 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