[理工] [線代]-線性轉換
True or False
For two square n * n matrices A and B , rank(AB) = rank(A) if and only if B
is nonsingular.
Sol: A= 1 0 B= 0 0 則AB= 0 0
0 0 0 0 0 0
則rank(AB)=rank(A)=0 但B不為非奇異 所以是False
感覺解答錯了,rank(A)應該是1吧? 怎麼會是0 那這題又怎麼解釋呢?
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