WBJEE · Maths · Matrices
Suppose, \(\alpha, \beta, \gamma\) are the roots of the equation \(\mathrm{x}^3+\mathrm{qx}+\mathrm{r}=0(\) with \(\mathrm{r} \neq 0)\) and they are in A.P. Then the rank of the matrix \(\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right)\) is
- A \(3\)
- B \(2\)
- C \(0\)
- D None of the above
Answer & Solution
Correct Answer
(D) None of the above
Step-by-step Solution
Detailed explanation
Here, \(\alpha+\beta+\gamma=0\) \(\left|\begin{array}{lll} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{array}\right|=-\left(\alpha^3+\beta^3+\gamma^3-3 \alpha \beta \gamma\right)=0(\because \alpha+\beta+\gamma=0)\) Given,…
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