∵ System of equation has non trivial solution. It is possible only when Δ=0.
∴Δ=∣1cc−c−1c−cc−1∣=0
⇒1(1−c2)+c(−c−c2)−c(c2+c)=0
⇒2c3+3c2−1=0
⇒c=−1,21
Hence, the greatest value of c=21.
The greatest value of c∈R for which the system of linear equations x−cy−cz=0, cx−y+cz=0, cx+cy−z=0 has a non-trivial solution, is
Held on 8 Apr 2019 · Verified 6 Jul 2026.
−1
2
21
0
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