TS EAMCET · Maths · Determinants
Let \(a, b, c \notin\{0,1\}\). If the system of equations
\(\begin{aligned} & \Pi_1 \equiv x+a y+a z=0 \\ & \Pi_2 \equiv b x+y+b z=0 \\ & \Pi_3 \equiv c x+c y+z=0\end{aligned}\)
has a non-trivial solution, then the system of equations \(\Pi_1=a, \Pi_2=b, \Pi_3=c\) has
- A unique solution
- B infinite number of solutions
- C no solution
- D unique solution only when \(a=b=c\)
Answer & Solution
Correct Answer
(D) unique solution only when \(a=b=c\)
Step-by-step Solution
Detailed explanation
Given system of equations has a non-trivial solution \(\begin{aligned} & \Pi_1 \equiv x+a y+a z=0 \\ & \Pi_2 \equiv b x+y+b z=0 \\ & \Pi_3 \equiv c x+c y+z=0\end{aligned}\) It can be written as \(A X=0\) Where,…
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