WBJEE · Maths · Determinants
The number of real values of \(\alpha\) for which the system of equations
\(
\begin{array}{l}
x+3 y+5 z=\alpha x \\
5 x+y+3 z=\alpha y
\end{array}
\)
\(3 x+5 y+z=\alpha z\)
has infinite number of solutions is
- A 1
- B 2
- C 4
- D 6
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
The system of equations are \[ \begin{array}{l} x+3 y+5 z=\alpha x \\ 5 x+y+3 z=\alpha y \\ 3 x+5 y+z=\alpha z \\ (1-\alpha) x+3 y+5 z=0 \\ 5 x+(1-\alpha) y+3 z=0 \\ 3 x+5 y+(1-\alpha) z=0 \end{array} \] For infinite number of solutions, we must have…
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