AP EAMCET · Maths · Determinants
If the set of equations \(x+2 y+3 z=6, x+3 y+5 z=9\), \(2 x+5 y+a z=b\) has unique solution, then
- A \(a=8, b=15\)
- B \(a \neq 8, b \in \mathrm{R}\)
- C \(a=8, b \neq 15\)
- D \(a \neq 15, b=8\)
Answer & Solution
Correct Answer
(B) \(a \neq 8, b \in \mathrm{R}\)
Step-by-step Solution
Detailed explanation
For unique solution \(\left|\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 5 & a\end{array}\right| \neq 0\) \(\begin{aligned} & \Rightarrow 3 a-25-2(a-10)+3(5-6) \neq 0 \\ & \Rightarrow a-8 \neq 0 \Rightarrow a \neq 8 \text { and } b \in R . \end{aligned}\)
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