JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The ordered pair \((a, b)\), for which the system of linear equations \(3 x-2 y+z=b\) ; \(5 x-8 y+9 z=3\) ; \(2 x+y+a z=-1\) has no solution, is
- A \(\left(3, \frac{1}{3}\right)\)
- B \(\left(-3, \frac{1}{3}\right)\)
- C \(\left(-3,-\frac{1}{3}\right)\)
- D \(\left(3,-\frac{1}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-3,-\frac{1}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc} 3 & -2 & 1 \\ 5 & -8 & 9 \\ 2 & 1 & a \end{array}\right|=0\) \(3(-8 a-9)+2(5 a-18)+1(21)=0\) \(\Rightarrow a=-3\) Also \(\Delta_{2}=\left|\begin{array}{ccc}3 & -2 & b^{\frac{1}{3}} \\ 5 & 8 & 3 \\ 2 & 1 & -1\end{array}\right|\) If \(b =\frac{1}{3}\)…
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