WBJEE · Maths · Linear Programming
Consider the system of equations
\(\begin{array}{cc}
x+y+z & =0 \\
\alpha x+\beta y+\gamma z & =0 \\
\alpha^{2} x+\beta^{2} y+\gamma^{2} z & =0
\end{array}\)
Then the system of equations has
- A a unique solution for all values of \(\alpha, \beta\) and \(\gamma\).
- B infinite number of solutions, if any two of \(\alpha, \bar{\beta},\) yare equal.
- C a unique solution, if \(\alpha, \beta\) and \(\gamma\) are distinct.
- D more than one, but finite number of solutions depending on values of \(\alpha, \beta\) and \(\gamma\)
Answer & Solution
Correct Answer
(C) a unique solution, if \(\alpha, \beta\) and \(\gamma\) are distinct.
Step-by-step Solution
Detailed explanation
Given system of equations is \(x+y+z=0\) \(\begin{array}{l} \alpha x+\beta y+\gamma z=0 \\ \alpha^{2} x+\beta^{2} y+\gamma^{2} z=0 \end{array}\) The coefficient matrix,…
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