[理工] [線代]-矩陣運算與行列式的証明
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.
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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※ 編輯: sea1985 來自: 140.116.236.43 (11/09 10:59)
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