Given that q2−pr<0,p>0, then the value of ∣∣
∣∣pqpx+qyqrqx+rypx+qyqx+ry0∣∣
∣∣ is
A
zero
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B
positive
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C
negative
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D
q2+pr
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Solution
The correct option is A negative Δ=∣∣
∣∣pqpx+qyqrqx+rypx+qyqx+ry0∣∣
∣∣ Applying R3→R3−xR1−yR2 Δ=∣∣
∣
∣∣pqpx+qyqrqx+ry00−((px+qy)+(qx+ry))∣∣
∣
∣∣=−((px+qy)+(qx+ry))(pr−q2)=(q2−pr)((px+qy)+(qx+ry)) As q2−pr<0 Δ<0