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Question
Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz
Solution
`|(y + z, z, y),(z, z + x, x),(y, x, x + y)|`
[Applying C1 → C1 + C2 + C3]
= `|(2(y + z), z, y),(2(z + x), z + x, x),(2(y + x), x, x + y)|`
= `2|(y + z, z, y),(z + x, z + x, x),(x + y, x, x + y)|`
[Applying C1 → C1 – C2]
= `2|(y, z, y),(0, z + x, x),(y, x, x + y)|`
[Applying C3 → C3 – C1]
= `2|(y, z, 0),(0, z + x, x),(y, x, x)|`
[Applying R3 → R3 – R1]
= `2|(y, z, 0),(0, z + x, x),(y, x - z, x)|`
= `2y[(z + x)x - x(x - z)]`
= `2y[2xz]`
= 4xyz
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