[線代] 希望有人有空能夠幫忙解一下
1.suppose that A is p*p and its rank k satisfies k<p. show that A is singular
2.let A be p*q. prove that A^T*A is singular if the rank of A is strictly less
than q.
3.suppose that B is p*q and that A is q*q and nonsingular.
Prove that the rank of BA equals the rank of B.
4.suppose that B is p*q and that A is p*p and nonsingular.
Prove that the rank of AB equals the rank of B.
5.show that the rank of A*A^T is less than or equal to the rank of A.
6.prove that the rank of A equals that of A^T by proving it first for
Gauss-reduced A and then, using problems 3&4, for general A.
7.show that, if A is singular, then A(adjA)=0 and (adjA)A=0, and five an
example of a singular matrix A with adjA not equals to 0(in order to show
that the result of this problem is true for other than trivial reasons).
8.prove that the adjoint of a singular matrix is singular.
有人有空可以幫忙翻譯嗎??
感激不盡
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※ 編輯: j04cj86 來自: 140.115.26.92 (01/09 19:33)