JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(x+y+a z=b\) \(2 x+5 y+2 z=6\) \(x+2 y+3 z=3\) has infinitely many solutions, then \(2 a+3 b\) is equal to \(...........\).
- A \(23\)
- B \(28\)
- C \(25\)
- D \(20\)
Answer & Solution
Correct Answer
(A) \(23\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{lll}1 & 1 & a \\ 2 & 5 & 2 \\ 1 & 2 & 3\end{array}\right|=0 \Rightarrow 11-4- a =0\) \(a=7\) \(\Delta_1=\left|\begin{array}{lll} b & 1 & a \\ 6 & 5 & 2 \\ 3 & 2 & 3\end{array}\right|=0 \Rightarrow 11 b -12-21=0\) \(b =3\) \(2 a+3 b=23\)
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