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# 07 - VV P 18 19 20 21 23 174 11 P P 109 119 j W,W 2...

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1 1 1 109 119 P P - 174 18, 19, 20, 21, 23. P VV , 3:30-5:30 1 : ª* 1108 ª*

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2 §3 §3- 1 Ker nel and I mage V V V F V n σ α σα σ σ σ σ = = } { Im . , ) ( 7 1 1 1 1 j · ª 1 1 1 1 j · ª * σ σ Im dim : 1 Im ( ) . n V F σ 5 ¸® Im ; , Im , , = , = , ( ) Im ; Im . k k k σ α β σ ξ η σξ α ση β α β σξ ση σ ξ η σ α σξ σ ξ σ 2200 5 + = + = + = = Q a a 1207
3 . , , ), , , ( Im ) 2 ( 1 1 1 1 1 V L n n ε ε σε σε = σ 1 1 1 : Im , , = = ( , , ), ; n i i i n i i n i proof V a a L α σ ξ σξ α ξ ε α σξ σε σε σε = = 5 = = Q M M 1 1 , , Im . n n i i i i i i b b β β σε σ ε σ = = = = ∴ ⊆ ∴ = ). , , ( ) dim( 1 n rank V σε σε σ =

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4 . , , . ) dim(Im ) 3 ( 1 1 1 1 1 n A rankA ε ε σ = σ . ) , , ( , , , , ) , , ( ) dim(Im 1 1 1 1 1 1 1 1 1 1 A A A n n n = = σε σε σε σε σε σε = σ M ) 0 ( } 0 { . , ) ( : 8 1 - σ = = σα α = σ σ σ σ V Ker F V n V V V V V V V . dim 1 σ σ Ker
5 . ) ( 1 : 1 1 1 F V Ker n σ < 1 2 ( ) , , ker , 0 0 n n V F A X AX σ ε ε α σ α σα < 2200 = = ° ± ε ι M ) ( r rankA = Y AX β σα = ← → = Q a a a 1 , , 0 , n r X X AX - = ± . ) , , ( 1 nullA Ker n ε ε = σ 1 1 2 ( , , ) ( , , , ). i n i n r X Ker L α ε ε σ α α α - = = M 1 1 ( , , )( , , ) n n r X X ε ε - = ⟨

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6 1 0 0 0 ker {( ) 0, , } V V σ β α σ α α σα α α - = + = + = σ n rankA n Ker Im dim ) dim( - = - = σ ) ( ) ( ], [ ) ( ], [ 1 3 x f x f x F X f
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