Question
If a,b,c are non – zero real numbers and if the equations (a-1) x = y + z, (b -1)y = z + x, (c - 1)z = x + y has a non trivial solution, then ab + bc + ca is equal to
Answer: Option B
:
B
For non trivial solution
∣∣
∣∣a−1−1−111−b1111−c∣∣
∣∣=0
Applying C1→C1−C3 and C2→C2−C3, then
∣∣
∣∣a010−b1cc1−c∣∣
∣∣=0⇒a(−b+bc−c)−0+c(0−b)=0⇒ab+bc+ca=abc
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:
B
For non trivial solution
∣∣
∣∣a−1−1−111−b1111−c∣∣
∣∣=0
Applying C1→C1−C3 and C2→C2−C3, then
∣∣
∣∣a010−b1cc1−c∣∣
∣∣=0⇒a(−b+bc−c)−0+c(0−b)=0⇒ab+bc+ca=abc
Was this answer helpful ?
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