JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(\alpha x+y+z=5, x+2 y+\) \(3 z=4, x+3 y+5 z=\beta\) has infinitely many solutions, then the ordered pair \((\alpha, \beta)\) is equal to:
- A \((1,-3)\)
- B \((-1,3)\)
- C \((1,3)\)
- D \((-1,-3)\)
Answer & Solution
Correct Answer
(C) \((1,3)\)
Step-by-step Solution
Detailed explanation
For infinitely many solutions, \(\Delta=0=\Delta_{ x }=\Delta_{ y }=\Delta_{ z }\) \(\Delta=\left|\begin{array}{lll}\alpha & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 5\end{array}\right|=0\) \(\Rightarrow \alpha(10-9)-1(5-3)+1(3-2)=0\) \(\Rightarrow \alpha-2+1=0\) \(\Rightarrow \alpha=1\)…
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