JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations
\(\begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4\end{aligned}\)
has infinitely many solutions, then the value of \(22 \beta-9 \alpha\) is :
- A 49
- B 31
- C 43
- D 37
Answer & Solution
Correct Answer
(B) 31
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}3 & 1 & \beta \\ 2 & \alpha & -1 \\ 1 & 2 & 1\end{array}\right|=0\) \(3 \alpha+4 \beta-\alpha \beta+3=0\) \(\Delta_3=\left|\begin{array}{ccc}3 & 1 & 3 \\ 2 & \alpha & -3 \\ 1 & 2 & 4\end{array}\right|=0\) \(9 \alpha+19=0\)…
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