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Question

Using properties of determinants, prove that:
∣ ∣1+a1111+b1111+c∣ ∣=abc+bc+ca+ab

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Solution

=∣ ∣1+a1111+b1111+c∣ ∣
R1R1R2R3R3R2
=∣ ∣ab011+b10bc∣ ∣
=a(c+bc+b)+bc
=ab+bc+ac+abc

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