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j det A = n<br />
i=1 (−1)i+j aij det(A ij )<br />
i det A = n<br />
j=1 (−1)i+j aij det(A ij )<br />
<br />
<br />
det A = d(A (1) , . . . , A (n) )<br />
=<br />
=<br />
n<br />
aij(−1) i+j−2 <br />
1 ∗<br />
d<br />
0 A ij<br />
i=1<br />
n<br />
i=1<br />
(−1) i+j aij det A ij ,<br />
<br />
A ∈ Mn(F) adj A n × n (i, j) <br />
(−1) i+j det A ij <br />
(adj A)A = (det A)I<br />
A A−1 = 1<br />
det A adj A<br />
<br />
j < k<br />
det A =<br />
n<br />
(adj A)jiaij = (adj A · A)jj.<br />
i=1<br />
0 = det(A (1) , . . . , A (k) , . . . , A (k) , . . . , A (n) )<br />
=<br />
n<br />
(adj A)jiaik<br />
i=1<br />
= (adj A · A)jk.<br />
1<br />
A det A = 0 <br />
adj A<br />
A −1 = 1<br />
det A<br />
det A<br />
adj A · A = I <br />
Ax = b m n <br />
A m × n b F m rank A =<br />
rank(A| b) n = rank A = rank(A| b) <br />
x = A −1 b <br />
m = n <br />
A ∈ Mn(F) Ax = b x =<br />
(x1, . . . , xn) T xi = 1<br />
detA det A îb i = 1, . . . , n A îb <br />
A i b
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