QJEEM19Ma431c: JEE Main 2019 Mathematics - Class 12 JEEM19Ma431c Solution: The greatest value of c ∈ R for which the system of linear…

Question

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The greatest value of c

\in

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 :

Accepted Answer

If the system of equations has non-trivial solutions, then

D = 0

| \begin{matrix} 1 & - c & - c \\ c & - 1 & c \\ c & c & - 1 \end{matrix} | = 0

\Rightarrow

(1 - c²) + c(-c - c²) - c(c² + c) = 0

\Rightarrow

(1 + c)(1 - c - 2c²) = 0

\Rightarrow

(1 + c)² (1 - 2c) = 0

\Rightarrow

c = -1 or

\frac{1}{2}

∴

Greatest value of c is

\frac{1}{2}

.

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