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Question

Using the property of determinants and without expanding, prove that
∣ ∣xax+ayby+bzcz+c∣ ∣=0

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Solution

Let Δ=∣ ∣xax+ayby+bzcz+c∣ ∣
Applying C2=C2+C1 we get,
Δ=∣ ∣xx+ax+ayy+by+bzz+cz+c∣ ∣=0
Since second and third collumn are same.

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