求该行列式的解.

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求该行列式的解.
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求该行列式的解.
求该行列式的解.

求该行列式的解.
a1 0 0 b1
0 a2 b2 0
0 b3 a3 0
b4 0 0 a4
①当a1=0时,
0 0 b1 a2 b2
行列式=-b4 a2 b2 0 = -b4b1 =-b4b1(a2a3-b2b3)
b3 a3 0 b3 a3
②当a1≠0时,
r4-b4/a1·r1得:
a1 0 0 b1
0 a2 b2 0
0 b3 a3 0
0 0 0 a4-b4·b1/a1
a2 b2 0
=a1 b3 a3 0
0 0 a4-b4b1/a1
a2 b2
=a1(a4-b4b1/a1)
b3 a3
=(a1a4-b1b4)(a2a3-b2b3)
当a1=0时,也满足
故行列式的值=(a1a4-b1b4)(a2a3-b2b3)