JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of linear equations
\( x+y+z=6\),
\(2x+5y+az=36\),
\(x+2y+3z=b \) has:
- A unique solution for \( a=8 \) and \( b=16 \)
- B infinitely many solutions for \( a=8 \) and \( b=14 \)
- C infinitely many solutions for \( a=8 \) and \( b=16 \)
- D unique solution for \( a=8 \) and \( b=14 \)
Answer & Solution
Correct Answer
(B) infinitely many solutions for \( a=8 \) and \( b=14 \)
Step-by-step Solution
Detailed explanation
If \(D=\left|\begin{array}{lll}1 & 1 & 1 \\ 2 & 5 & a \\ 1 & 2 & 3\end{array}\right|=0 \Rightarrow a=8\) If \(D _1=\left|\begin{array}{ccc}6 & 1 & 1 \\ 36 & 5 & a \\ b & 2 & 3\end{array}\right|=0 \Rightarrow ab -5 b-12 a +54=0\) If…
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