Question

The greatest value of c ε 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 ______.

पर्याय

• –1

• 2

• `1/2`

• 0

Answer 1

The greatest value of c ε 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 `underlinebb(1/2)`.

Explanation:

For non-trivial solution,

D = 0

`|(1, -c, -c),(c, -1, c),(c, c, -1)|` = 0

1(1 – c²) + c(–c – c²) –c(c² + c) = 0

1 – c² – c² – c³ – c³ – c² = 0

1 – 3c² – 2c³ = 0

2c³ + 3c² – 1 = 0

By remainder theorem

(c + 1)²(2c – 1) = 0

c = `-1, 1/2`

Greatest value of c = `1/2`