行列代数2010A
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1 a ij i j 1) i +j i, j) ij ij 1 j a i1 a ij a i a 1 a j a ij 1) i +j 1,j 1,j +1 a i1,1 a i1,j 1 a i1,j +1 a i1, a i +1,1 a i +1.j 1 a i +1,j +1 a i +1, a 1 a,j 1 a,j +1 a,
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3 i 1i + i 2i ++ a i i i 1j + i 2j ++ a i j 0 for i j a ki ki a ki 1 0 a k1 1 a k 1 0 a k1 a ki a k a ki ki k1 1 i a i1 a ii a i a 1 0 a a 1 0 a a 1 a i a a ki kj a ki 1 0 a k1 1 a k a 1 0 a 1 0 a k1 a ki a k a 1 0 a a ki kj k1 1 i j 1 i i a i1 a ii a ii a i a j1 a ji a ji a j 1 a 1 a i a i a i j ij à t E [ a ij ], t [ ij ], k1 a ik jk [ ij ] E [ a ij ], t [ ij ], k1 a ki kj [ ij ] E
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6 cos si 0 si cos x cos, cos 2 + si ) 1+1 cos cos, 12 1) 1+2 si si, 13 1) ) 2 +1 si) si, 22 1) 2 +2 cos cos, 23 1) ) , 32 1) , 33 1) 3 +3 cos 2 + si 2 ) cos si )si cos y si x cos +) cos cos si si x cos y si y si +) cos si + si cos xsi + y cos z z x x y y z z x x y )1 y z z cos si 0 )1 )si cos ) x x a b z a + bi T b a 1 z z a + bi a b a T 1 + T* ) - T, b 1 a bi) a ) T T a b bi + b 2 b, 1 a b a a b + * - 1 a bi) ), a bi a + bi)a bi) 1 a + bi 1 z. T 1 1 z
7 P B O D 0, D 0 P BD 1 O D 1 X X 11 X 12 PX E 2 P 1 X X 21 X 22 PX X 11 + BX 21 X 12 + BX 22 E O DX 21 DX 22 O E X 11 + BX 21 E, X 12 + BX 22 O, DX 21 O, DX 22 E DX 21 O D X 21 O DX 22 E D X 22 D 1 X 11 + BX 21 E, X 21 O X 11 1 X 12 + BX 22 O X 12 1 BX 22 1 BD 1 P BD 1 O D 1 XP E 2 1 O 1, 2,..., 2 p O p X 11 X 12 X 1p 1 O X X 21 X 21 X 2p, 2 X p1 X p2 X pp O p 1 O X 11 X 12 X 1p 1 X 11 1 X 12 1 X 1p X 2 X 21 X 21 X 2p 2 X 21 2 X 22 2 X 2p O p X p1 X p2 X pp p X p1 p X p2 p X pp i i X ii 1 1 X ii i i X ij 0 X ij 1 i O ij O ij i ) j) * 1 O O p 1 1 E E E
8 b 2 + c 2 ab ac ba c 2 + bc ca cb + b 2 a,b,ca,b,c b 2 + c 2 ab ac ba c 2 + bc abc ca cb + b 2 b 2 + c 2 a a a b c 2 + b b c c + b 2 c b 2 + c 2 b 2 c 2 c 2 + c 2 b 2 + b 2 0 b 2 c 2 2c 2 c 2 + c 2 2 2b 2 b 2 + b 2 0 b 2 c 2 c 2 c 2 + c 2 2 b 2 b 2 + b 2 0 b 2 c 2 c 2 c 2 b b 2 2 4a 0 b 2 c 2 c b 2 c 2 b 2 0 x x x x 1 a 4 a 0 a 0 x 4 + x 3 + x 2 + x 1 + a 4 x x x x 1 a 4 a x 2 x x x 1 a 4 + x a 0 x x x 1 a 4 + x a x 3 x x 1 x x 1 a 4 + x + x 2 a 0 a 4 + x + x 2 a x 4 x 1 a 4 + x + x 2 + x 3 a 0 x 4 1 a 4 + x + x 2 + x 3 a 0 a 4 + x + x 2 + x 3 + a 0 x 4
9 O C D D ij P O C D P )* ) 1* 1) 2* 2) * ) + * i* i) 0 for i, p ad *i) > p - i, p. *i), p ) 1,p) ) 1,2,q) / * 0 *1),*p) p + 1) p,p + 2) p,) p ) ) ) P ) 1 1) 2 2) ) ) ) 1 1) 2 2) p p) p+1) p+1) p+ 2) p+ 2) ), ) 1 1) 2 2) p p) ) p+1) p+1) p+ 2) p+ 2) ) D I p I q p i) p 0 i p p i p i i) p 1 1) 2 2) ) 0 B B + B B B B ib + ib B B + B B B + + B B 0 B + B B B B ib B B + i ib B 0 + ib ib + ib
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11 xx a 3 B a 3 b 11 b 21 b 22 b 31 b 32 b 11 + b 21 + b 31 + b 22 + b 32 a 3 B b 11 + b 21 + b 31 + b 22 + b 32 b 11 b 22 + b 11 b 32 + b 21 + b 21 b 32 + b 31 + b 31 b 22 b 11 b 22 b 21 ) + b 11 b 32 b 31 ) + b 21 b 32 b 31 b 22 ) b 11 b 21 b 22 + b 11 b 31 b 32 + b 21 b 22 b 31 b 32 k 1,k 2 )b b k1 1 k 2 2 a k1 a k2 + k 1,k 2 )b b k1 1 k 2 2 a k1 a k2 + k 1,k 2 )b b k1 1 k 2 2 a k1 a k2 1k 1 <k 2 2 1k 1 <k 2 3 2k 1 <k 2 3 k 1,k 2 )b b k1 1 k 2 2 a k1 a k2 1k 1 <k 2 3 f i x), g i x),h i x) d dx d dx d dx f 1 x) g 1 x) f 2 x) g 2 x) f 1 x) g 1 x) f 2 x) g 2 x) + f 1 x) g 1 x) f 2 x) g 2 x) f 1 x) g 1 x) h 1 x) f 3 x) g 3 x) h 3 x) f 1 x) g 1 x) h 1 x) f 2 x) g 2 x) h 2 x) f 2 x) g 2 x) h 2 x) + f 3 x) g 3 x) h 3 x) f 1 x) g 1 x) f 2 x) g 2 x) d dx f 1x)g 2 x) g 1 x) f 2 x) f 1x) g 1 x) f 2 x) g 2 x) + f 1x) g 1 x) f 2 x) g 2 x) d dx f 1 x) g 1 x) h 1 x) f 2 x) g 2 x) h 2 x) f 3 x) g 3 x) h 3 x) f 1 x) g 1 x) h 1 x) f 2 x) g 2 x) h 2 x) f 3 x) g 3 x) h 3 x) f 1 x) g 1 x) h 1 x) + f 2 x) g 2 x) h 2 x) f 3 x) g 3 x) h 3 x) ) f 1 x)g 2 x) g 1 x) f 2 x)) + f 1 x) g 2 x) g 1 x) f 2 x)) d dx f 1 g 2 h 3 + f 2 g 3 h 1 + f 3 g 1 h 2 f 3 g 2 h 1 f 2 g 1 h 3 f 1 g 3 h 2 ) ) + f 1 g 2 h 3 + f 2 g 3 h 1 + f 3 g 1 h 2 f 3 g 2 h 1 f 2 g 1 h 3 f 1 g 3 h 2 ) + f 1 g 2 h 3 + f 2 g 3 h 1 + f 3 g 1 h 2 f 3 g 2 h 1 f 2 g 1 h 3 f 1 ) f 1 g 2 h 3 + f 2 g 3 h 1 + f 3 g 1 h 2 f 3 g 2 h 1 f 2 g 1 h 3 f 1 g 3 h 2 f 1 x) g 1 x) h 1 x) f 2 x) g 2 x) h 2 x) + f 3 x) g 3 x) h 3 x) f 1 x) g 1 x) h 1 x) f 2 x) g 2 x) h 2 x) f 3 x) g 3 x) h 3 x) g 3 h 2 f 1 x) g 1 x) h 1 x) + f 2 x) g 2 x) h 2 x) f 3 x) g 3 x) h 3 x)
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(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
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04年度LS民法Ⅰ教材改訂版.PDF
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LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y
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AHPを用いた大相撲の新しい番付編成
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熊本県数学問題正解
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福岡大学人文論叢47-3
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高校生の就職への数学II
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取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ
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高等学校学習指導要領解説 数学編
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ORIGINAL TEXT I II A B 1 4 13 21 27 44 54 64 84 98 113 126 138 146 165 175 181 188 198 213 225 234 244 261 268 273 2 281 I II A B 292 3 I II A B c 1 1 (1) x 2 + 4xy + 4y 2 x 2y 2 (2) 8x 2 + 16xy + 6y 2
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x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
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1 40 (1959 1999 ) (IMO) 41 (2000 ) WEB 1 1959 1 IMO 1 n, 21n + 4 13n + 3 2 (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a = 4, b =
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章 複素数平面 1: ポイント整理 PMYA1-Z1J1-01 学習時間のめやす 45 分 1. 複素数平面 < 1-1 複素数平面 > a = a+ bi a b xy ^a bh xy 1 ^a bh a = a+ bi 複素数平面 x 実軸 y 虚軸 a A A ^ a h 点 a O < 1 - 共役な複素数 > a = a+ bi a b a-bi a 共役な複素数 a a a = ^a+
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ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD
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HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】
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