→ sea1985:thank you very much^__^ 11/10 09:51
※ 引述《sea1985 (海嗨咍)》之銘言：
: 不好意思 有幾題不太懂 請有空的大大幫我解題 ^__^
: 1.回答對或錯
: The solution set of any system of m linear equations in n unknows is
: a subspace of F^n.
: 答案是false,因為n<m的時候 有可能no solutions?
: 2.Prove that if A is an invertible upper triangular matrix
: then the classical adjoint of A and A^-1 are upper triangular.
2.adj(A)=C^T
Cij=(-1)^(i+j)Mij
Cij is Aij cofactor
aussue A is upper tri matrix
A=[aij] when i>j ,aij is zero
s.t. Cij when i<j is zero => C is lower tri matrix
C^T is upper tri matrix ,so adj(A) is upper tri matrix
1
A^-1=------adj(A) ,A^-1 is also upper tri matrix
det(A)
: 3.Let k=\=0 be a nonzero number,show hy induct that for all positive integers n.
: n
: [cos(x) ksin(x)] = [cos(nx) ksin(nx)]
: [(-1/k)*sin(x) cos(x)] [(-1/k)*sin(nx) cos(nx) ]
: 4.(a)Find all real matrices A for which (A^T)A=0{A的轉置*A=0}
: (b)Find all matrices B for which (B^H)B=0{A的Hermitian*A=0}
: 5.Prove that
: (a).If A has a full row of zeros,then A has no right inverse.
: (b).If A has a full column of zeros,then A has no left inverse.
: (c).If A is square and either a full row or a full column of zeros,then A is
: singular.
: 不好意思 我自己一個人唸書 所以沒有趴惹可以問 麻煩各位大大有空幫忙解答
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◆ From: 123.193.214.165
※ 編輯: iyenn 來自: 123.193.214.165 (11/09 13:33)
※ 編輯: iyenn 來自: 123.193.214.165 (11/09 13:35)