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Question

If ∣∣ ∣∣pq−yr−zp−xqr−zp−xq−yr∣∣ ∣∣=0, then the value of px+qy+rz is

A
0
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B
1
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C
2
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D
4pqrs
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Solution

The correct option is C 2
Dividing C1,C2,C3 by x,y,z we have
=xyz∣ ∣ ∣ ∣ ∣ ∣pxqy1rz1px1qyrz1px1qy1rz∣ ∣ ∣ ∣ ∣ ∣=0
Applying C1C1+C2+C3
=xyz∣ ∣ ∣ ∣ ∣ ∣px2qy1rz1px2qyrz1px2qy1rz∣ ∣ ∣ ∣ ∣ ∣=0
xyz(px2)∣ ∣ ∣ ∣ ∣ ∣1qy1rz11qyrz11qy1rz∣ ∣ ∣ ∣ ∣ ∣=0
Using R1R1R2,R2R2R3 then expanding with the help of third Row (R3) we get px=2
i.e. px+qy+rz=2
Hence choice (c) is correct.

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