{"id":28862,"date":"2025-11-29T06:02:24","date_gmt":"2025-11-28T21:02:24","guid":{"rendered":"https:\/\/lanqiu.aboutphlaw.com\/?p=28862"},"modified":"2025-11-29T06:02:24","modified_gmt":"2025-11-28T21:02:24","slug":"3x3-matrix-inverse-calculation-methods-and-applications-5","status":"publish","type":"post","link":"https:\/\/lanqiu.aboutphlaw.com\/3x3\/3x3-matrix-inverse-calculation-methods-and-applications-5","title":{"rendered":"3&#215;3 \u884c\u5217 \u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3068\u305d\u306e\u5fdc\u7528\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059"},"content":{"rendered":"<h4>1. 3&#215;3 \u884c\u5217\u306e\u57fa\u672c\u6982\u5ff5<\/h4>\n<p>3&#215;3\u884c\u5217\u306f\u30013\u3064\u306e\u884c\u30683\u3064\u306e\u5217\u3092\u6301\u3064\u6b63\u65b9\u884c\u5217\u3067\u3001\u6570\u5b66\u3084\u7269\u7406\u5b66\u3001\u5de5\u5b66\u306a\u3069\u69d8\u3005\u306a\u5206\u91ce\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e00\u822c\u7684\u306a3&#215;3\u884c\u5217\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u884c\u5217A = <br \/>\n\\(\\beginpmatrix a_11 &#038; a_12 &#038; a_13 \\\\ a_21 &#038; a_22 &#038; a_23 \\\\ a_31 &#038; a_32 &#038; a_33 \\endpmatrix\\)<\/p>\n<p>\u3053\u3053\u3067\u3001\u5404\u8981\u7d20\\(a_ij\\)\u306f\u5b9f\u6570\u3084\u8907\u7d20\u6570\u3067\u3001\u884c\u5217\u306e\u5404\u4f4d\u7f6e\u3092\u793a\u3057\u307e\u3059\u30023&#215;3\u884c\u5217\u306f\u3001\u7dda\u5f62\u4ee3\u6570\u306b\u304a\u3044\u3066\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5909\u63db\u3001\u7cfb\u306e\u89e3\u6cd5\u3001\u30c7\u30fc\u30bf\u306e\u6271\u3044\u306a\u3069\u3001\u975e\u5e38\u306b\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>2. \u9006\u884c\u5217\u306e\u5b9a\u7fa9\u3068\u8a08\u7b97\u65b9\u6cd5<\/h4>\n<p>\u9006\u884c\u5217\u3068\u306f\u3001\u3042\u308b\u884c\u5217A\u306b\u5bfe\u3057\u3066\u3001\u305d\u306e\u884c\u5217\u3092\u639b\u3051\u308b\u3068\u5358\u4f4d\u884c\u5217I\u306b\u306a\u308b\u3088\u3046\u306a\u884c\u5217B\u3092\u6307\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001AB = I\u306a\u3089\u3070\u3001B\u304cA\u306e\u9006\u884c\u5217\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u30023&#215;3\u884c\u5217\u306e\u9006\u884c\u5217\u306f\u3001\u7279\u5b9a\u306e\u5f0f\u3092\u7528\u3044\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u884c\u5217A\u306e\u9006\u884c\u5217A^-1\u306f\u3001\u6b21\u306e\u5f0f\u3092\u7528\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>A^-1 = \\(\\frac1\\textdet(A) \\cdot \\textadj(A)\\)<\/p>\n<p>\u3053\u3053\u3067\u3001det(A)\u306f\u884c\u5217A\u306e\u884c\u5217\u5f0f\u3001adj(A)\u306f\u968f\u4f34\u884c\u5217\u3092\u793a\u3057\u307e\u3059\u30023&#215;3\u884c\u5217\u306e\u884c\u5217\u5f0f\u306f\u3001\u884c\u5217\u306e\u5404\u8981\u7d20\u3092\u7528\u3044\u3066\u8a08\u7b97\u3055\u308c\u3001\u7279\u306b\u3001\u884c\u5217\u304c\u975e\u7279\u7570\uff08\u884c\u5217\u5f0f\u304c0\u3067\u306a\u3044\uff09\u3067\u3042\u308b\u9650\u308a\u3001\u9006\u884c\u5217\u306f\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<h4>3. \u9006\u884c\u5217\u306e\u5177\u4f53\u7684\u306a\u8a08\u7b97\u4f8b<\/h4>\n<p>\u4f8b\u3048\u3070\u3001\u884c\u5217A\u304c\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>A = \\(\\beginpmatrix 1 &#038; 2 &#038; 3 \\\\ 0 &#038; 1 &#038; 4 \\\\ 5 &#038; 6 &#038; 0 \\endpmatrix\\)<\/p>\n<p>\u307e\u305a\u3001\u884c\u5217\u306e\u884c\u5217\u5f0f\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u9006\u884c\u5217\u306e\u5b58\u5728\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u3001\u968f\u4f34\u884c\u5217\u3092\u6c42\u3081\u3001\u6700\u5f8c\u306b\u9006\u884c\u5217\u3092\u6c42\u3081\u308b\u3068\u3044\u3046\u624b\u9806\u3067\u9032\u3081\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u5177\u4f53\u7684\u306a\u8a08\u7b97\u3092\u901a\u3058\u3066\u3001\u9006\u884c\u5217\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h4>4. \u9006\u884c\u5217\u306e\u5fdc\u7528\u4f8b<\/h4>\n<p>\u9006\u884c\u5217\u306f\u3001\u69d8\u3005\u306a\u5206\u91ce\u3067\u306e\u5fdc\u7528\u304c\u3042\u308a\u3001\u7279\u306b\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u7dda\u5f62\u4ee3\u6570\u306e\u4e2d\u3067\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0fAx = b\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001A\u306e\u9006\u884c\u5217\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u7c21\u5358\u306b\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3059\u306a\u308f\u3061\u3001x = A^-1b\u3068\u306a\u308a\u3001\u9006\u884c\u5217\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\u591a\u304f\u306e\u60c5\u5831\u3092\u4e00\u62ec\u3057\u3066\u89e3\u6c7a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6d3b\u304b\u3057\u3066\u3001\u7269\u7406\u5b66\u3084\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30b9\u306b\u304a\u3044\u3066\u3082\u9006\u884c\u5217\u306f\u591a\u304f\u306e\u8a08\u7b97\u306b\u5229\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>5. \u6570\u5b66\u6559\u80b2\u306b\u304a\u3051\u308b\u9006\u884c\u5217\u306e\u91cd\u8981\u6027<\/h4>\n<p>\u9006\u884c\u5217\u306e\u7406\u89e3\u306f\u3001\u6570\u5b66\u6559\u80b2\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u3002\u7279\u306b\u9ad8\u6821\u3084\u5927\u5b66\u3067\u5b66\u3076\u7dda\u5f62\u4ee3\u6570\u3067\u306f\u3001\u9006\u884c\u5217\u306e\u6982\u5ff5\u304c\u5f8c\u306e\u591a\u304f\u306e\u5b66\u554f\u306b\u5f79\u7acb\u3064\u57fa\u76e4\u3068\u306a\u308a\u307e\u3059\u3002\u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u7fd2\u5f97\u3059\u308b\u3053\u3068\u3067\u3001\u5b66\u751f\u306f\u6570\u5b66\u7684\u601d\u8003\u3092\u6df1\u3081\u3001\u554f\u984c\u89e3\u6c7a\u80fd\u529b\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u9006\u884c\u5217\u306e\u5b66\u7fd2\u3092\u901a\u3058\u3066\u3001\u5b9f\u751f\u6d3b\u306e\u69d8\u3005\u306a\u554f\u984c\u306b\u5bfe\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u8003\u3048\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u3001\u6570\u5b66\u306e\u9b45\u529b\u3092\u3088\u308a\u4e00\u5c64\u611f\u3058\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002\u3053\u306e\u3088\u3046\u306b\u30013&#215;3 \u884c\u5217 \u9006\u884c\u5217\u306e\u5b66\u7fd2\u306f\u3001\u5358\u306a\u308b\u8a08\u7b97\u3092\u8d85\u3048\u305f\u6df1\u3044\u7406\u89e3\u3092\u4fc3\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30bf\u30a4\u30c8\u30eb3&#215;3 \u884c\u5217 \u9006\u884c\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3068\u305d\u306e\u5fdc\u7528\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059<\/p>\n","protected":false},"author":1,"featured_media":1166,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[4823,6796,15190],"class_list":["post-28862","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3x3","tag-3x3","tag-6796","tag-15190"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>3x3 \u884c\u5217 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