WBJEE · Maths · Determinants
Under which of the following condition(s) does(do) the system of equations \(\left(\begin{array}{ccc}1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & (a-4)\end{array}\right)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}6 \\ 4 \\ a\end{array}\right)\) possesses (possess) unique solution?
- A \(\forall \mathrm{a} \in \mathrm{R}\)
- B \(a=8\)
- C for all integral values of a
- D \(a \neq 8\)
Answer & Solution
Correct Answer
(D) \(a \neq 8\)
Step-by-step Solution
Detailed explanation
\(\Delta \neq 0\) \(\Rightarrow\left|\begin{array}{ccc} 1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & \mathrm{a}-4 \end{array}\right| \neq 0 \Rightarrow \mathrm{a} \neq 8\)
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