{"id":462,"date":"2012-11-02T12:13:02","date_gmt":"2012-11-02T03:13:02","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=462"},"modified":"2021-10-03T15:59:55","modified_gmt":"2021-10-03T06:59:55","slug":"kbr201005","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201005\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2010\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(a\\) \u3092\u5b9f\u6570\u3068\u3057, \\(A = \\left( \\begin{array}{cc} a+1 & a \\\\ 3 & a+2 \\end{array} \\right)\\) \u3068\u3059\u308b. \\(2\\) \u70b9 \\(P (x,y)\\) , \\(Q (X,Y)\\) \u306b\u3064\u3044\u3066\r\n\\[\r\n\\left( \\begin{array}{c} X \\\\ Y \\end{array} \\right) = A \\left( \\begin{array}{c} x \\\\ y \\end{array} \\right)\r\n\\]\r\n\u304c\u6210\u308a\u7acb\u3064\u3068\u304d, \\(P\\) \u306f \\(A\\) \u306b\u3088\u308a \\(Q\\) \u306b\u79fb\u308b\u3068\u3044\u3046.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u539f\u70b9\u4ee5\u5916\u306e\u70b9\u3067, \\(A\\) \u306b\u3088\u308a\u305d\u308c\u81ea\u8eab\u306b\u79fb\u308b\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3068\u304d, \\(a\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6b21\u306e\u6761\u4ef6 (\uff0a) \u3092\u307f\u305f\u3059 \\(a , k\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n

      \r\n
    1. (\uff0a)\u3000\u76f4\u7dda \\(\\ell : \\ y = kx+1\\) \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u306f, \\(A\\) \u306b\u3088\u308a \\(\\ell\\) \u4e0a\u306e\u70b9\u306b\u79fb\u308b.<\/li>\r\n<\/ol><\/li>\r\n

    2. (3)<\/strong>\u3000(\uff0a) \u3092\u307f\u305f\u3059 \\(a , k\\) \u306b\u5bfe\u3057, \u76f4\u7dda \\(\\ell\\) \u4e0a\u306e\u70b9\u3067, \\(A\\) \u306b\u3088\u308a\u305d\u308c\u81ea\u8eab\u306b\u79fb\u308b\u3082\u306e\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

      \r\n\r\n

      \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

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

      \\[\\begin{align}\r\nA \\left( \\begin{array}{c} x \\\\ y \\end{array} \\right) & = \\left( \\begin{array}{c} x \\\\ y \\end{array} \\right) \\\\\r\n(A-E) \\left( \\begin{array}{c} x \\\\ y \\end{array} \\right) & = \\left( \\begin{array}{c} 0 \\\\ 0 \\end{array} \\right)\r\n\\end{align}\\]\r\n\u3053\u308c\u304c \\(\\left( \\begin{array}{c} x \\\\ y \\end{array} \\right) \\neq \\left( \\begin{array}{c} 0 \\\\ 0 \\end{array} \\right)\\) \u3067\u3042\u308b\u89e3\u3092\u3082\u3064\u306e\u306f, \u9006\u884c\u5217 \\((A-E)^{-1}\\) \u304c\u5b58\u5728\u3057\u306a\u3044\u3068\u304d\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\det (A-E) = a(a+1) -3a & = 0 \\\\\r\na^2-2a & = 0 \\\\\r\na(a-2) & = 0 \\\\\r\n\\text{\u2234} \\quad a & = \\underline{0 , 2}\r\n\\end{align}\\]\r\n

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

      \\(\\ell\\) \u4e0a\u306e\u70b9\u306f\u5b9f\u6570 \\(t\\) \u3092\u7528\u3044\u3066, \\(( t , kt+1 )\\) \u3068\u8868\u305b\u308b.\r\n\\[\\begin{align}\r\nA \\left( \\begin{array}{c} t \\\\ kt+1 \\end{array} \\right) & = \\left( \\begin{array}{c} (a+1)t +a(kt+1) \\\\ 3t +(a+2)(kt+1) \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{c} (ak+a+1)t +a \\\\ (ak+2k+3)t +a+2 \\end{array} \\right)\r\n\\end{align}\\]\r\n\u3053\u306e\u70b9\u3082 \\(\\ell\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n(ak+2k+3)t +a+2 & = k \\left\\{ (ak+a+1)t +a \\right\\} +1 \\\\\r\n\\text{\u2234} \\quad (ak^2-k-3)t & +ak -a-1 = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u3059\u3079\u3066\u306e \\(t\\) \u306b\u3064\u3044\u3066\u6210\u7acb\u3059\u308b\u306e\u3067\r\n\\[\r\nak^2-k-3 = 0 \\quad ... [1] , \\ ak-a-1 = 0 \\quad ... [2]\r\n\\]\r\n[2] \u3088\u308a \\(k \\neq 1\\) \u306a\u306e\u3067\r\n\\[\r\na = \\dfrac{1}{k-1} \\quad ... [3]\r\n\\]\r\n[1] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{k^2}{k-1} & -k -3 = 0 \\\\\r\nk^2 & = (k-1)(k+3) \\\\\r\n\\text{\u2234} \\quad k & = \\underline{\\dfrac{3}{2}}\r\n\\end{align}\\]\r\n[3] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\r\na = \\dfrac{1}{\\frac{3}{2}-1} = \\underline{2}\r\n\\]\r\n

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

      (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\nA = \\left( \\begin{array}{cc} 3 & 2 \\\\ 3 & 4 \\end{array} \\right) , \\ \\ell : \\ y = \\dfrac{3}{2}x +1\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{gather}\r\n\\left( \\begin{array}{cc} 3 & 2 \\\\ 3 & 4 \\end{array} \\right) \\left( \\begin{array}{c} x \\\\ \\dfrac{3}{2}x +1 \\end{array} \\right) = \\left( \\begin{array}{c} x \\\\ \\dfrac{3}{2}x +1 \\end{array} \\right) \\\\\r\n\\text{\u2234} \\quad \\left\\{ \\begin{array}{l} 3x +3x+2 =x \\\\ 3x +6x +4 = \\dfrac{3}{2}x +1 \\end{array} \\right.\r\n\\end{gather}\\]\r\n\\(2\\) \u5f0f\u306f\u3044\u305a\u308c\u3082\r\n\\[\\begin{align}\r\n5x+2 & = 0 \\\\\r\n\\text{\u2234} \\quad x & = -\\dfrac{2}{5}\r\n\\end{align}\\]\r\n\\(\\ell\\) \u306e\u5f0f\u3088\u308a\r\n\\[\r\ny = \\dfrac{3}{2} \\left( -\\dfrac{2}{5} \\right) +1 = \\dfrac{5}{2}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u70b9\u306f\r\n\\[\r\n\\underline{\\left( -\\dfrac{2}{5} , \\dfrac{2}{5} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u5b9f\u6570\u3068\u3057, \\(A = \\left( \\begin{array}{cc} a+1 & a \\\\ 3 & a+2 \\end{array} \\right)\\) \u3068\u3059\u308b. \\(2\\) \u70b9 \\(P (x,y)\\) … \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":[40],"tags":[144,14],"class_list":["post-462","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2010","tag-tsukuba_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/462","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=462"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/462\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=462"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=462"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}