\u884c\u5217\r\n\\[\r\nA = \\left( \\begin{array}{cc} 3 & -1 \\\\ 4 & -1 \\end{array} \\right)\r\n\\]\r\n\u306e\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3059\u308b.\r\n\\(f\\) \u306b\u3088\u308b\u70b9 P \\((1,1)\\) \u306e\u50cf\u3092 \\(\\text{P} {} _ 1\\) \u3068\u3059\u308b.\r\n\u6b63\u306e\u6574\u6570 \\(n\\) \u306b\u5bfe\u3057, \\(\\text{P} {} _ n\\) \u306e \\(f\\) \u306b\u3088\u308b\u50cf\u3092 \\(\\text{P} {} _ {n+1}\\) \u3068\u3059\u308b.\r\n\\(\\text{P} {} _ n\\) \u304c\u70b9 \\((10, 10)\\) \u306b\u6700\u3082\u8fd1\u304f\u306a\u308b\u3068\u304d\u306e \\(n\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n
\\(\\text{P} {} _ n \\ ( x _ n , y _ n )\\) , \\(\\text{P} = \\text{P} {} _ 0\\) \u3068\u304a\u304f.\r\n\\[\r\n\\left( \\begin{array}{c} x _ 1 \\\\ y _ 1 \\end{array} \\right) = \\left( \\begin{array}{cc} 3 & -1 \\\\ 4 & -1 \\end{array} \\right) \\left( \\begin{array}{c} 1 \\\\ 1 \\end{array} \\right) = \\left( \\begin{array}{c} 2 \\\\ 3 \\end{array} \\right) \\ .\r\n\\]\r\n\u307e\u305f\r\n\\[\r\n\\left( \\begin{array}{c} x _ {n+1} \\\\ y _ {n+1} \\end{array} \\right) = \\left( \\begin{array}{cc} 3 & -1 \\\\ 4 & -1 \\end{array} \\right) \\left( \\begin{array}{c} x _ n \\\\ y _ n \\end{array} \\right) = \\left( \\begin{array}{c} 3 x _ n -y _ n \\\\ 4 x _ n -y _ n \\end{array} \\right) \\ .\r\n\\]\r\n\u3053\u3053\u304b\u3089\r\n\\[\r\ny _ n = 3 x _ n -x _ {n+1} \\quad ... [1] \\ .\r\n\\]\r\n\u306a\u306e\u3067, \u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n3 x _ {n+1} -x _ {n+2} & = 4 x _ n -( 3x _ n -x _ {n+1} ) \\\\\r\n\\text{\u2234} \\quad x _ {n+2} -x _ {n+1} & = x _ {n+1} -x _ {n} \\ .\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u7e70\u8fd4\u3057\u7528\u3044\u308c\u3070\r\n\\[\r\nx _ {n+1} -x _ n = x _ 1 -x _ 0 = 1 \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nx _ n = x _ 0 +n = n+1 \\ .\r\n\\]\r\n[1] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\r\ny _ n = 3(n+1) -(n+2) = 2n+1 \\ .\r\n\\]\r\n\\(\\text{P} {} _ n\\) \u3068\u70b9 \\((10, 10)\\) \u306e\u8ddd\u96e2\u306e\u5e73\u65b9\u3092 \\(f(n)\\) \u3068\u304a\u304d, \\(f(n)\\) \u3092\u6700\u5c0f\u306b\u3059\u308b\u81ea\u7136\u6570 \\(n\\) \u3092\u6c42\u3081\u308c\u3070\u3088\u3044.\r\n\\[\\begin{align}\r\nf(n) & = ( 10-x _ n )^2 +( 10-y _ n )^2 \\\\\r\n& = ( 9-n )^2 +( 9-2n )^2 \\\\\r\n& = 5n^2 -54n +162 \\\\\r\n& = 5 \\left( n -\\dfrac{27}{5} \\right)^2 +162 -\\dfrac{27^2}{5} \\ .\r\n\\end{align}\\]\r\n\\(f(n)\\) \u306f \\(n\\) \u306e \\(2\\) \u6b21\u95a2\u6570\u3067\u3042\u308a, \\(\\dfrac{27}{5} =5.4\\) \u306a\u306e\u3067, \\(f(n)\\) \u3092\u6700\u5c0f\u3068\u3059\u308b, \u3059\u306a\u308f\u3061\u6c42\u3081\u308b\u81ea\u7136\u6570\u306f\r\n\\[\r\nn = \\underline{5} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u884c\u5217 \\[ A = \\left( \\begin{array}{cc} 3 & -1 \\\\ 4 & -1 \\end{array} \\right) \\] \u306e\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3059\u308b. \\(f\\) \u306b\u3088\u308b … \u7d9a\u304d\u3092\u8aad\u3080