Tiểu luận: ÁNH XẠ TUYẾN TÍNH TOÁN CAO CẤP A2

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Tiểu luận: ÁNH XẠ TUYẾN TÍNH  TOÁN CAO CẤP A2

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[%;,= R  3\$+]  Ánh xa tuyên tinh ^  _ Đnh ngha nh x tuyn tnh R'` "#$$LA<5>R→ `$: ,=/a( =4> _7 56b7E567b567' '∈ R8 c7 567E'∈ , ∈ R B5>R→ ` ,=D> 56__bcc7E_56_7bc56c7'_'c∈ , c∈ R B5>`ER'5>R→ R$: .,=R c Cc php ton v nh x tuyn tnh @.5>R→ ` $>R→ ` c,=>  d$;c,= ∈ R865b$767E567b$67∈ `8  =;5Ke'"=  ?> ∈ R'6E∈ `  R'`'f g"#$$LA5>R→ ` $>`→ R c,= Y/9?> ∈ R'6$ . 5767E$6567∈ f ()*RfB9;c () ,= g Ma trn ca axtt: 5>R→ ` ,=D> !EFL _ 'L c hL  H A;R !iEFLi _ 'Li c hLi  H A;`'/∈ R' E _ L _ b c L c bhb  L   j./>567E _ 56L _ 7  b c 56L c 7  bhb  56L  7    Ánh xa tuyên tinh T?56L _ 7h56L  7+ki 56L _ 7E __ Li _ b c_ Li c b g_ Li g bhb (_ Li  56L c 7E _c Li _ b c_ Li c b g_ Li g bhb (c Li ( hhhhh 56L  7E _ Li _ b c Li c b g Li g bhb ( Li (  Y/(%>  __  _c h _ E  c_  cc h c :);56L _ 7]  (_  (c h ( $: (%;5KlA67 ^  _ Dng 1: C/m f l# m$t nh x tuyn tnh  !"#$%&'() *#&+*,  /0 1 20 1 /3  4  4 1 563  7 1 4  485 E6 _ ' c ' g 7∈ k g ,E6, _ ', c ', g 7∈ k g b,E6 _ b, _ ' c  b, c ' g b, g 7 56b,7E6 _ b, _ X g X, g ' c  b, c 'm7 567E56 _ ' c ' g 7E6 _ X g ' c 'm7 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c ', c 'q c 7∈ k g  bE6 _ b c ', _ b, c 'q _ bq c 7 ∈ k g 56b7E56 _ b c ', _ b, c 'q _ bq c 7 E6 _ b c ', _ b, c 'Xq _ Xq c 7 E6 _ ', _ 'Xq _ 7 + 6 c ' c 'Xq c 7E567b567 56o7E56o _ 'o, _ 'oq _ 7E6o _ 'o, _ 'Xoq _ 7 Eo6 _ ', _ 'Xq _ 7 = o567 R,5 ,= L /  /3;56;<; * CQEr s t  ∈ [  8!Er s t  ∈ [  D b!Er s b s t  ∈ [   56b!7E6b!7b6b!7  E6b!7b6  b!  7 E6b  7b6!b!  7E567b56!7 56o7E6o7b6o7  Eobo  Eo6b  7Eo567 R,5 ,= 5 /=2= /3>56><#4#?@AB*>C*D$EF CQ _ '   c ∈ R  _ b   c ∈ R 56 _ b c 7E6 _ b c 7b8 56 _ 7b56 c 7E6 _ b7b6 c b7E _ b c bcj.u 56 _ b c 7u56 _ 7b56 c 7 R,5"#$ ,= G Ánh xa tuyên tinh $ /24$EHI/356 1 56b,7E6b,7 g u567b56,7 R,5"#$ ,=  /  2  $EHI/J(35K6(35<(L35F 5r67b+67tEr67b+67tbr67b+67ti Er67bi67tbr+67b+i67t E5r67b5r+67t 5ro67tEo67b6o677iEo667bi677Eo5r67t R,5 ,= c Dng 2: T'm ma trn ca f @0$(%v$5> c 2 c '? 56 _ 8 c 7E6 _ Xw c ' _ b c 7 ().,= D((%;5x ) CQE6 _ 8 c 7∈ c 8,E6, _ 8, c 7∈ c y,%>b,E6 _ b c ', _ b, c 7 ∈ k c 56b,7E56 _ b, _ ' c b, c 7 E66 _ b, _ 7Xw6 c b, c 7'6 _ b, _ 7'6 c b, c 77 E66 _ Xw c 7b6, _ pw, c 7'6 _ b c 7b6, _ b, c 77 E6 _ Xw c ' _ b c 7b6, _ pw, c ', _ b, c 7 E567b56,7 56o7E6o6 _ Xw c 7'o6 _ b c 77Eo6 _ Xw c ' _ b c 7 Eo567 R,5 ().,= @A=-; c   !EFL _ E6_'n7'L c E6n'_7H !iEFLi _ E6_'n7'Li c E6n'_7H /> 56L _ 7E56_'n7E6_'_7EL _ bL c 56L c 7E56n'_7E6Xw'_7EXwL _ bL c R,>[%;.5 > E @0$(%v$5> g 2 g '? 56 _ ' c ' g 7E6c _ '   c pg g 7 ().,= D((%;5x ) 8 Ánh xa tuyên tinh CQE6 _ 8 c 8 g 7∈ w 8,E6, _ 8, c 8, g 7∈ w y,%>b,E6 _ b, _ ' c b, c ' g b, g 7 ∈ k c 56b,7E56 _ b, _ ' c b, c ' g b, g 7 E6c6 _ b, _ 7'6 c b, c 7'6g g p, g 77 567E56 _ 8 c 8 g 7 E56c _ ' c pg g 7 56,7E56, _ 8, c 8, g 7E56c, _ 8, c Xg, g 7 56b,7E567b56,7 56o7E6oc _ 'o6 c pg g 7Eo6c _ ' c pg g 7 Eo567 R,5 ,= @A=-; g   !EFL 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Từ khóa liên quan

Mục lục

  • MỞ ĐẦU

  • x = (x1, x2, x3) R3

  • y = (y1, y2, y3) R3

  • x + y = (x1 + y1, x2 + y2, x3 + y3)

  • f(x + y) = (x1 + y1 - x3 - y3, x2 + y2, 5)

  • f(x) = f(x1, x2, x3) = (x1 - x3, x2, 5)

  • f(y) = f(y1, y2, y3) = (y1 - y3, y2, 5)

  • f(x) + f(y) = (x1 + y1 - x3 - y3, x2 + y2, 10)

  • Vậy f(x + y) khác f(x) + f(y) R3

  • f(x1, x2, x3) = (x2 - x3, x1, x2)

  • x = (x1, x2, x3) R3

  • y = (y1, y2, y3) R3

  • x + y = (x1 + y1, x2 + y2, x3 + y3)

  • f(x) = f(x1, x2, x3) = (x2 - x3, x1, x2)

  • f(y) = f(y1, y2, y3) = (y2 - y3, y1, y2)

  • Như vậy: f(x + y) = f(x) + f(y) R3

  • λx = (λx2 – λx3, λx1, λx2)

  • = λ(x2 - x3, x1, x2)

  • = λ.f(x)

  • Vậy f là ánh xạ tuyến tính

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