JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(\mathrm{x}+4 \mathrm{y}-\mathrm{z}=\lambda\), \(7 x+9 y+\mu z=-3,5 x+y+2 z=-1\) has infinitely many solutions, then \((2 \mu .+3 \lambda)\) is equal to :
- A \(2\)
- B \(-3\)
- C \(3\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(-3\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}1 & 4 & -1 \\ 7 & 9 & \mu \\ 5 & 1 & 2\end{array}\right|=0\) \(\Rightarrow(18-\mu)-4(14-5 \mu)-(7-45)=0 \Rightarrow \mu=0\) \(\Delta=\Delta_{\mathrm{x}}=\Delta_{\mathrm{y}}=\Delta_{\mathrm{z}}=0\) (For infinite solution)…
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