If the equations x = ay + z, y = az + x

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

If the equations x = ay + z, y = az + x and z = ax + y are consistent having non-trivial solution, then

Options:

a³ = 1

a³ + 1 = 0

a + 1 = 0

None of these

Correct Answer:

None of these

Explanation:

$\Delta=\left|\begin{array}{ccc}1 & -a & -1 \\ -1 & 1 & -a \\ -a & -1 & 1\end{array}\right|=0$

⇒ a³ – 3a = 0

Hence (4) is the correct answer.