{"id":81,"date":"2011-11-26T22:55:51","date_gmt":"2011-11-26T13:55:51","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=81"},"modified":"2021-09-30T10:01:17","modified_gmt":"2021-09-30T01:01:17","slug":"kbr201105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201105\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2011\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u5b9f\u6570\u3092\u6210\u5206\u3068\u3059\u308b\u884c\u5217 \\(A = \\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3092\u8003\u3048\u308b.\r\n\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 \\(P \\ ( x , y )\\) , \\(Q \\ ( u , v )\\) \u306b\u3064\u3044\u3066\u7b49\u5f0f\r\n\\[\r\n\\left( \\begin{array}{c} u \\\\ v \\end{array} \\right) = A \\left( \\begin{array}{c} x \\\\ y \\end{array} \\right)\r\n\\]\r\n\u304c\u6210\u308a\u7acb\u3064\u3068\u304d, \u884c\u5217 \\(A\\) \u306b\u3088\u308a\u70b9 \\(P\\) \u306f\u70b9 \\(Q\\) \u306b\u79fb\u308b\u3068\u3044\u3046.\r\n\u70b9 \\(( 1 , 3 )\\) \u306f\u884c\u5217 \\(A\\) \u306b\u3088\u308a\u70b9 \\(( 10 , 10 )\\) \u306b\u79fb\u308a, \u3055\u3089\u306b\u7b49\u5f0f\r\n\\[\r\nA^2 -7A +10E = O\r\n\\]\r\n\u304c\u6210\u308a\u7acb\u3064\u3082\u306e\u3068\u3059\u308b. \u305f\u3060\u3057, \\(E = \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & 1 \\end{array} \\right)\\) , \\(O = \\left( \\begin{array}{cc} 0 & 0 \\\\ 0 & 0 \\end{array} \\right)\\) \u3067\u3042\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u884c\u5217 \\(A\\) \u306b\u3088\u308a \\(( 10 , 10 )\\) \u304c\u79fb\u308b\u70b9\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5b9f\u6570 \\(a , b , c , d\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u6b21\u306e\u6761\u4ef6 (\uff0a) \u3092\u6e80\u305f\u3059\u76f4\u7dda \\(l\\) \u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u3088.\r\n

      \r\n

    1. (\uff0a) \u76f4\u7dda \\(l\\) \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u304c\u884c\u5217 \\(A\\) \u306b\u3088\u308a \\(l\\) \u4e0a\u306e\u70b9\u306b\u79fb\u308b.<\/p><\/li>\r\n<\/ol><\/li>\r\n<\/ol>\r\n

      \r\n\r\n

      \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

      (1)<\/strong><\/p>\r\n

      \u79fb\u308b\u70b9\u3092 \\(( p , q )\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\n\\left( \\begin{array}{c} p \\\\ q \\end{array} \\right) & = A \\left( \\begin{array}{c} 10 \\\\ 10 \\end{array} \\right) = A^2 \\left( \\begin{array}{c} 1 \\\\ 3 \\end{array} \\right) = \\left( 7A -10E \\right) \\left( \\begin{array}{c} 1 \\\\ 3 \\end{array} \\right) \\\\\r\n& = 7 \\left( \\begin{array}{c} 10 \\\\ 10 \\end{array} \\right) -10 \\left( \\begin{array}{c} 1 \\\\ 3 \\end{array} \\right) = \\left( \\begin{array}{c} 60 \\\\ 40 \\end{array} \\right)\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, R \\(\\underline{( 60 , 40 )}\\) .<\/p>\r\n

      (2)<\/strong><\/p>\r\n

      (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\r\nA \\left( \\begin{array}{cc} 1 & 10 \\\\ 3 & 10 \\end{array} \\right) = \\left( \\begin{array}{cc} 10 & 60 \\\\ 10 & 40 \\end{array} \\right) \\quad ... [1]\r\n\\]\r\n\\(\\left( \\begin{array}{cc} 1 & 10 \\\\ 3 & 10 \\end{array} \\right)\\) \u306e\u9006\u884c\u5217\u306f\r\n\\[\r\n\\left( \\begin{array}{cc} 1 & 10 \\\\ 3 & 10 \\end{array} \\right)^{-1} = \\dfrac{1}{10-30} \\left( \\begin{array}{cc} 10 & -10 \\\\ -3 & 1 \\end{array} \\right) = \\dfrac{1}{20} \\left( \\begin{array}{cc} -10 & 10 \\\\ 3 & -1 \\end{array} \\right)\r\n\\]\r\n\u3053\u308c\u3092 [1] \u306e\u4e21\u8fba\u306b\u53f3\u304b\u3089\u639b\u3051\u308c\u3070\r\n\\[\\begin{align}\r\nA & = \\dfrac{1}{20} \\left( \\begin{array}{cc} 10 & 60 \\\\ 10 & 40 \\end{array} \\right) \\left( \\begin{array}{cc} -10 & 10 \\\\ 3 & -1 \\end{array} \\right) \\\\\r\n&= \\dfrac{1}{20} \\left( \\begin{array}{cc} 80 & 40 \\\\ 20 & 60 \\end{array} \\right) = \\left( \\begin{array}{cc} 4 & 2 \\\\ 1 & 3 \\end{array} \\right)\r\n\\end{align}\\]\r\n\u3086\u3048\u306b\r\n\\[\r\na = \\underline{4} , \\ b = \\underline{2} , \\ c = \\underline{1} , \\ d = \\underline{3}\r\n\\]\r\n

      (3)<\/strong><\/p>\r\n

      \u76f4\u7dda \\(l\\) \u306e\u8868\u3057\u65b9\u306b\u3088\u3063\u3066, \u5834\u5408\u5206\u3051\u3057\u3066\u8003\u3048\u308b.<\/p>\r\n

        \r\n

      1. 1*<\/strong>\u3000\\(x = a\\) \u306e\u3068\u304d, \u76f4\u7dda\u4e0a\u306e\u70b9\u306f \\(( a , t )\\) \u3068\u8868\u305b\u308b.\r\n\\[\r\n\\left( \\begin{array}{cc} 4 & 2 \\\\ 1 & 3 \\end{array} \\right) \\left( \\begin{array}{c} a \\\\ t \\end{array} \\right) = \\left( \\begin{array}{c} 4a+2t \\\\ a+3t \\end{array} \\right)\r\n\\]\r\n\u3053\u308c\u304c \\(l\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n4a+2t & = a \\\\\r\n\\text{\u2234} \\quad 2t +3a & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u306f\u4efb\u610f\u306e \\(t\\) \u306b\u3064\u3044\u3066, \u6210\u308a\u7acb\u305f\u306a\u3044\u306e\u3067\u4e0d\u9069.<\/p><\/li>\r\n

      2. 2*<\/strong>\u3000\\(y = px+q\\) \u306e\u3068\u304d, \u76f4\u7dda\u4e0a\u306e\u70b9\u306f \\(( t , pt+q )\\) \u3068\u8868\u305b\u308b.\r\n\\[\r\n\\left( \\begin{array}{cc} 4 & 2 \\\\ 1 & 3 \\end{array} \\right) \\left( \\begin{array}{c} t \\\\ pt+q \\end{array} \\right) = \\left( \\begin{array}{c} 2(p+2)t +2q \\\\ (3p+1)t +3q \\end{array} \\right)\r\n\\]\r\n\u3053\u308c\u304c \\(l\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n(3p+1)t +3q = p\\left\\{ (3p+1)t +3q \\right\\} & +q \\\\\r\n(2p^2+p-1)t +2pq-2q & = 0 \\\\\r\n(2p-1)(p+1)t +2q(p-1) & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u4efb\u610f\u306e \\(t\\) \u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u3064\u306e\u3067,\r\n\\[\\begin{gather}\r\n\\left\\{ \\begin{array}{l} (2p-1)(p+1)=0 \\\\ 2q(p-1)=0 \\end{array} \\right. \\\\\r\n\\text{\u2234} \\quad ( p , q ) = \\left( \\dfrac{1}{2} , 0 \\right) , ( -1 , 0 )\r\n\\end{gather}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\r\n\\[\r\n\\underline{y = \\dfrac{1}{2}x , \\ y = -x}\r\n\\]<\/li>\r\n<\/ol>\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570\u3092\u6210\u5206\u3068\u3059\u308b\u884c\u5217 \\(A = \\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3092\u8003\u3048\u308b. \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 \\(P \\ ( x … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","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":[41],"tags":[144,13],"class_list":["post-81","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2011","tag-tsukuba_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/81","targetHints":{"allow":["GET"]}}],"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=81"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/81\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=81"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=81"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=81"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}