The greatest value of c Î R for which the system of linear equations x – cy – cz = 0 cx – y + cz = 0 cx + cy

Engineering

Mathematics

Solving System of Linear Equation Cramers Rule

Question

The greatest value of c Î 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

–1

$\frac{1}{2}$

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For non – trivial solution

D = 0

$| \begin{matrix} 1 & - c & - c \\ c & - 1 & c \\ c & c & - 1 \end{matrix} | = 0 \Rightarrow 2 c^{2} + 3 c^{2} - 1 = 0$

⇒ (c + 1)² (2c – 1) = 0

$∴$ Greatest value of c is $\frac{1}{2}$