※ 引述《sea1985 (海嗨咍)》之铭言： : 不好意思 有几题不太懂 请有空的大大帮我解题 ^__^ : 1.回答对或错 : The solution set of any system of m linear equations in n unknows is : a subspace of F^n. : 答案是false,因为n<m的时候 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的转置*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 我自己一个人念书 所以没有趴惹可以问 麻烦各位大大有空帮忙解答 -- 为者常成.行者常至 --

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