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determinant expansion by minors

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Let a,b,c,d,e,f,g,h be reals. Prove that the following matrix A is singular.

Matrix A: 0 a 0 0 0
b 0 c 0 0
0 d 0 e 0
0 0 f 0 g
0 0 0 h 0

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Laplace's formula (determinant expansion by minors) is presented.

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