{"id":54,"date":"2011-11-26T18:17:50","date_gmt":"2011-11-26T09:17:50","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=54"},"modified":"2021-09-16T05:36:51","modified_gmt":"2021-09-15T20:36:51","slug":"ngr201102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201102\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2011\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(A _ 0 = \\left( \\begin{array}{cc} 0 & 0 \\\\ 0 & 0 \\end{array} \\right)\\) \u3068\u3059\u308b. \u6574\u6570 \\(n \\geqq 1\\) \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u8a66\u884c\u306b\u3088\u308a\u884c\u5217 \\(A _ {n-1}\\) \u304b\u3089\u884c\u5217 \\(A _ n\\) \u3092\u5b9a\u3081\u308b.<\/p>\r\n<ol>\r\n<li>\u300c\u3000\u6570\u5b57\u306e\u7d44 \\(( 1 , 1 )\\) , \\(( 1 , 2 )\\) , \\(( 2 , 1 )\\) , \\(( 2 , 2 )\\) \u3092 \\(1\\) \u3064\u305a\u3064\u66f8\u3044\u305f \\(4\\) \u679a\u306e\u672d\u304c\u5165\u3063\u3066\u3044\u308b\u888b\u304b\u3089 \\(1\\) \u679a\u3092\u53d6\u308a\u51fa\u3057, \u305d\u306e\u672d\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u6570\u5b57\u306e\u7d44\u304c \\(( i , j )\\) \u306e\u3068\u304d, \\(A _ {n-1}\\) \u306e \\(( i , j )\\) \u6210\u5206\u306b \\(1\\) \u3092\u52a0\u3048\u305f\u884c\u5217\u3092 \\(A _ n\\) \u3068\u3059\u308b.\u3000\u300d<\/li>\r\n<\/ol>\r\n<p>\u3053\u306e\u8a66\u884c\u3092 \\(n\\) \u56de\uff08 \\(n = 2 , 3 , 4 , \\cdots\\) \uff09\u304f\u308a\u8fd4\u3057\u305f\u5f8c\u306b, \\(A _ 0 , A _ 1 , \\cdots , A _ {n-1}\\) \u304c\u9006\u884c\u5217\u3092\u3082\u305f\u305a \\(A _ n\\) \u306f\u9006\u884c\u5217\u3092\u3082\u3064\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(p _ 2\\) , \\(p _ 3\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\((n-1)\\) \u56de\uff08 \\(n = 2 , 3 , 4 , \\cdots\\) \uff09\u306e\u8a66\u884c\u3092\u304f\u308a\u8fd4\u3057\u305f\u5f8c\u306b, \\(A _ {n-1}\\) \u306e\u7b2c \\(1\\) \u884c\u306e\u6210\u5206\u304c\u3044\u305a\u308c\u3082\u6b63\u3067\u7b2c \\(2\\) \u884c\u306e\u6210\u5206\u306f\u3044\u305a\u308c\u3082 \\(0\\) \u3067\u3042\u308b\u78ba\u7387 \\(p _ {n-1}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(p _ n\\) \uff08 \\(n = 2 , 3 , 4 , \\cdots\\) \uff09\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n\r\n    <div id='extLink54'>\r\n        <p>\r\n            <a href='https:\/\/www.roundown.net\/nyushi\/ngr201102\/' name='ext54' onclick=\"showHide(54,'https:\/\/www.roundown.net\/nyushi\/ngr201102\/',this,'entry');return false;\">\u89e3\u7b54\u306f\u3053\u3061\u3089 &#187;<\/a>\r\n        <\/p>\r\n    <\/div>\r\n    <div id='extText54' style='display: none'>\r\n        \r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(n\\) \u56de\u76ee\u306b\u521d\u3081\u3066 \\(|A _ n| \\neq 0\\) \u3068\u306a\u308b\u5834\u5408\u3092\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\u884c, \u5217\u306e\u3044\u305a\u308c\u3092\u5165\u66ff\u3048\u3066\u3082, \\(|A _ n|\\) \u306e\u5024\u306f\u5909\u308f\u3089\u306a\u3044\u306e\u3067, \\(1\\) \u56de\u76ee\u306b\u306f \\(( 1 , 1 )\\) \u304c\u51fa\u308b\u3068\u8003\u3048\u3066\u3082, \u4e00\u822c\u6027\u3092\u5931\u308f\u306a\u3044.<br \/>\r\n\\(p _ 2\\) \u306b\u3064\u3044\u3066, \\(2\\) \u56de\u76ee\u306b \\(( 2 , 2 )\\) \u304c\u51fa\u308c\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\np _ 2 = \\underline{\\dfrac{1}{4}}\n\\]\r\n\\(p _ 3\\) \u306b\u3064\u3044\u3066, \\(3\\) \u56de\u76ee\u306b<\/p>\r\n<ul>\r\n<li><p>\\(A _ 2 = \\left( \\begin{array}{cc} 2 & 0 \\\\ 0 & 0 \\end{array} \\right)\\) \u304b\u3089 \\(( 2 , 2 )\\)<\/p><\/li>\r\n<li><p>\\(A _ 2 = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & 0 \\end{array} \\right)\\) \u304b\u3089 \\(( 2 , 1 )\\) \u307e\u305f\u306f \\(( 2 , 2 )\\)<\/p><\/li>\r\n<li><p>\\(A _ 2 = \\left( \\begin{array}{cc} 1 & 0 \\\\ 1 & 0 \\end{array} \\right)\\) \u304b\u3089 \\(( 1 , 2 )\\) \u307e\u305f\u306f \\(( 2 , 2 )\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u304c\u51fa\u308c\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\np _ 3 = \\dfrac{1}{4} \\cdot \\dfrac{1}{4} +\\dfrac{1}{4} \\cdot \\dfrac{1}{2} +\\dfrac{1}{4} \\cdot \\dfrac{1}{2} =\\underline{\\dfrac{5}{16}}\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(4\\) \u679a\u306e\u3046\u3061, \\(( 1 , 1 )\\) , \\(( 1 , 2 )\\) \u306e \\(2\\) \u679a\u306e\u307f\u304c\u51fa\u308c\u3070\u3088\u3044.<br \/>\r\n\u305f\u3060\u3057, \u3069\u3061\u3089\u304b\u4e00\u65b9\u306e\u307f\u304c\u51fa\u308b\u5834\u5408\u306f\u9664\u304f\u306e\u3067,\r\n\\[\r\nq _ {n-1} = \\underline{\\left( \\dfrac{1}{2} \\right)^{n-1} -2\\left( \\dfrac{1}{4} \\right)^{n-1}}\n\\]\r\n<p><strong>(3)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u3068\u540c\u69d8\u306b, \\(1\\) \u56de\u76ee\u306b \\(( 1 , 1 )\\) \u304c\u51fa\u305f\u3068\u3057\u3066\u8003\u3048\u308b.<br \/>\r\n\\(|A _ {n-1}| =0\\) \u3068\u306a\u308b\u884c\u5217\u306f, \u4ee5\u4e0b\u306e \\(3\\) \u30d1\u30bf\u30fc\u30f3\u304c\u3042\u308a, \u305d\u308c\u305e\u308c\u306b\u5bfe\u3057\u3066 \\(n\\) \u56de\u76ee\u306b<\/p>\r\n<ul>\r\n<li><p>\\(A _ {n-1} =\\left( \\begin{array}{cc} n-1 & 0 \\\\ 1 & 0 \\end{array} \\right)\\) \u304b\u3089 \\(( 2 , 2 )\\)<\/p><\/li>\r\n<li><p>\\(A _ {n-1} =\\left( \\begin{array}{cc} n-1-k & k \\\\ 0 & 0 \\end{array} \\right) \\quad ( 1 \\leqq k \\leqq n-2 )\\) \u304b\u3089 \\(( 2 , 1 )\\) \u307e\u305f\u306f \\(( 2 , 2 )\\)<\/p><\/li>\r\n<li><p>\\(A _ {n-1} =\\left( \\begin{array}{cc} n-1-k & 0 \\\\ k & 0 \\end{array} \\right) \\quad ( 1 \\leqq k \\leqq n-2 )\\) \u304b\u3089 \\(( 1 , 2 )\\) \u307e\u305f\u306f \\(( 2 , 2 )\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u304c\u51fa\u308c\u3070\u3088\u3044.<br \/>\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\np _ n & = \\left( \\dfrac{1}{4} \\right)^{n-2} \\cdot \\dfrac{1}{4} +2 \\left\\{ \\left( \\dfrac{1}{2} \\right)^{n-2} -\\left( \\dfrac{1}{4} \\right)^{n-2} \\right\\} \\cdot \\dfrac{1}{2} \\\\\r\n& = \\underline{\\left( \\dfrac{1}{2} \\right)^{n-2} -\\dfrac{3}{4} \\left( \\dfrac{1}{4} \\right)^{n-2}}\n\\end{align}\\]\r\n\r\n        <p>\r\n            <a href='#ext54' onclick=\"showHide(54,0,this,'entry');return true;\">&#171; \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n        <\/p>\r\n    <\/div>","protected":false},"excerpt":{"rendered":"\\(A _ 0 = \\left( \\begin{array}{cc} 0 &#038; 0 \\\\ 0 &#038; 0 \\end{array} \\right)\\) \u3068\u3059\u308b. \u6574\u6570 \\(n \\geqq 1\\) \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u8a66\u884c\u306b\u3088\u308a\u884c\u5217  [&hellip;]","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[35],"tags":[143,13],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/54"}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=54"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/54\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=54"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=54"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}