作者smartlwj (实变我好爱你)
看板Grad-ProbAsk
标题Re: [理工] [工数] 矩阵证明
时间Thu Sep 24 19:51:51 2009
※ 引述《cmkv7rdf (Why so serious?)》之铭言：
: 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
(a) assume that A:mxn B:nxp C:pxq matrix
n n p
(A(BC))_ij = sigma a_ik(BC)_kj = sigma a_ik[sigma b_kl c_ij]
k=1 k=1 l=1
n p p n
= sigma sigma a_ik b_kl c_lj = sigma sigma a_ik b_kl c_lj
k=1 l=1 l=1 k=1
p n p
= sigma [sigma a_ik b_kl]c_ij = sigma (AB)_il c_lj
l=1 k=1 l=1
=((AB)C)_ij i=1~m j=1~q
(b)(c)用同样的方式可以得到结论
: 3.let A=│ a11 a12 │ ,show that if d=a11a22-a21a12≠0,
: │ a21 a22 │
: Then A^-1= 1/d │ a22 -a12 │
: │ -a21 a11 │
: 回答出来一题给100P
use A^(-1) = adj(A)/det(A)
adj(A) = [ a22 -a12]
[-a21 a11]
since d = a11a22-a21a12 ≠0
then A^(-1) = adj(A)/det(A) = (1/d)[ a22 -a12]
[-a21 a11]
这应该是课本上的定理或习题
自己翻书看看
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