Re: [理工] [周易]線代
det[adj(A)] = det|2 0 0 0| = 2*det| 2 1 0|
|0 2 1 0| | 4 3 2|
|0 4 3 2| |-2-1 2|
|0-2-1 2|
= |B|*|C|
with B = |2|
C = | 2 1 0|
| 4 3 2|
|-2-1 2|
=> |B|=2 and |C|=4
so det[adj(A)] = |B|*|C| = 8
= det[|A|*A^(-1)] 這步是定理,可自行證明
= (|A|^4)*det[A^(-1)]
= (|A|^4)*(|A|^(-1))
= |A|^3
=> |A|=2
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