线性代数求助.设A为n阶矩阵,且lAl=2,则llAlA^Tl=答案为2^n+1,但我不明白怎样做.

Question

线性代数求助.设A为n阶矩阵,且lAl=2,则 l lAlA^T l= 答案为2^n+1,但我不明白怎样做.

Answer 1

||A|A^T|
= |A|^n |A^T| --性质:|kA| = k^n|A|
= |A|^n |A| --性质:|A^T| = |A|
= |A|^(n+1)
= 2^(n+1)