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Question

If x,y,z are different from zero and Δ=∣ ∣abyczaxbczaxbyc∣ ∣=0, then the value of the expression ax+by+cz is ?

A
0
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B
1
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C
1
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D
2
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Solution

The correct option is D 2
Δ=∣ ∣abyczaxbczaxbyc∣ ∣=0
xyz∣ ∣ ∣ ∣axby1cz1ax1bycz1ax1by1cz∣ ∣ ∣ ∣=0
∣ ∣ ∣ ∣axby1cz1ax1bycz1ax1by1cz∣ ∣ ∣ ∣=0
C1C1+C2+C3
∣ ∣ ∣ ∣ax+by+cz2by1cz1ax+by+cz2bycz1ax+by+cz2by1cz∣ ∣ ∣ ∣=0
(ax+by+cz2)∣ ∣ ∣ ∣1by1cz11bycz11by1cz∣ ∣ ∣ ∣=0
R1R1R2,R2R2R3
(ax+by+cz2)∣ ∣ ∣0100111by1cz∣ ∣ ∣=0
(ax+by+cz2)=0
ax+by+cz=2

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