Re: [理工] [工數] 矩陣證明

[smartlwj (實變我好愛你)]

※ 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.

(0,0,0)' in R^3  , so S is nonempty

for any a,b in R , and (x1,x2,x3)' (y1,y2,y3)' in S

then
     a(x1,x2,x3)' + b(y1,y2,y3)'

   = (ax1,ax2,ax3)' + (by1,by2,by3)'

   = (ax1+by1,ax2+by2,ax3+by3)'

since x1=x2 and y1=y2 , so ax1+by1 =ax2+by2

and hence a(x1,x2,x3)' + b(y1,y2,y3)' in S

i.e. 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

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◆ From: 123.195.16.32
※ 編輯: smartlwj        來自: 123.195.16.32        (09/24 19:36)
推 cmkv7rdf:感恩!!隨後奉上100P