作者iyenn (曉風)
看板Grad-ProbAsk
標題Re: [理工] [工數] 矩陣證明
時間Thu Sep 24 20:26:08 2009
※ 引述《cmkv7rdf (Why so serious?)》之銘言：
: 1.let S ={(x1,x2,x3)′│x1=x2} . Show that S is a subspace of R^3.
: 2.prove the following rules for matrix multiplication:
: (a) (AB)C=A(BC)
: (b) A(B+C)=AB+AC
: (c) (AB) = B A
: 3.let A=│ a11 a12 │ ,show that if d=a11a22-a21a12≠0,
: │ a21 a22 │
: Then A^-1= 1/d │ a22 -a12 │
: │ -a21 a11 │
: 回答出來一題給100P
來用牛刀,騙騙p幣= =
Q=[a11 a12]
[a21 a22]
設E=[A B]
[C D]
QE=EQ=I
即B=Q^-1
即a11A+a12C=1 ....(1) Aa11+Ba21=1 ....(5)
a11B+a12D=0 ....(2) Aa12+Ba22=0 ....(6)
a21A+a22C=0 ....(3) Ca11+Da21=0 ....(7)
a21B+a22D=1 ....(4) Ca12+Da22=1 ....(8)
由(1)xa22-(3)xa12
=a11a22A-a12a21A=a22
=>A=a22/(a11a22-a12a21)=a22/d
代回(3)(6)
得C=-a21/d
得B=-a12/d
由(2)
得D=a11/d
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◆ From: 123.193.214.165
※ 編輯: iyenn 來自: 123.193.214.165 (09/24 20:27)
1F：推 cmkv7rdf:肛溫!!謝謝! 09/24 20:28