WBJEE · Maths · Determinants
If the following three linear equations have a non-trivial solution, then
\[
\begin{array}{l}
x+4 a y+a z=0 \\
x+3 b y+b z=0 \\
x+2 c y+c z=0
\end{array}
\]
- A \(a, b, c\) are in \(A P\)
- B \(a, b, c\) are in \(G\)
- C \(a, b, c\) are in \(\mathrm{HP}\)
- D \(a+b+c=0\)
Answer & Solution
Correct Answer
(C) \(a, b, c\) are in \(\mathrm{HP}\)
Step-by-step Solution
Detailed explanation
For non-trivial solution, We have, \(\left|\begin{array}{ccc}1 & 4 a & a \\ 1 & 3 b & b \\ 1 & 2 c & c\end{array}\right|=0\) \(\Rightarrow \quad 1(3 b c-2 b c)-(4 a c-2 a c)+1(4 a b-3 a b)=0\) \(\Rightarrow b c-2 a c+a b=0\) \(\Rightarrow b c+a b=2 a c\)…
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