The system of equation kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to:

The system of equation kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to:

Option 1 - 0

Option 2 - 1

Option 3 - -2

Option 4 - -1

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Answered by

Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

The system of equations has no solution if the determinant of the coefficient matrix is zero.
Δ = |k 1|
|1 k 1|
|1 k|
Δ = k (k² - 1) - 1 (k - 1) + 1 (1 - k) = 0
Δ = k³ - k - k + 1 + 1 - k = 0
⇒ k³ - 3k + 2 = 0 ⇒ (k - 1)² (k + 2) = 0
∴ k = -2, 1
If k = 1 then all the equations are identical (infinite soluti

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Kindly consider the following figure

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