JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For the system of equations \(x+y+z=6\) \(x+2 y+\alpha z=10\) \(x+3 y+5 z=\beta\), which one of the following is NOT true?
- A System has a unique solution for \(\alpha=3, \beta \neq 14\).
- B System has no solution for \(\alpha=3, \beta=24\).
- C System has a unique solution for \(\alpha=-3, \beta=14\).
- D System has infinitely many solutions for \(\alpha=3\), \(\beta=14\).
Answer & Solution
Correct Answer
(A) System has a unique solution for \(\alpha=3, \beta \neq 14\).
Step-by-step Solution
Detailed explanation
\(x+y+z\) \(x+2 y+\alpha z=10\) \(x+3 y+5 z=\beta\) \(D=\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & \alpha \\ 1 & 3 & 5\end{array}\right|=1(10-3 \alpha)-1(5-\alpha)+1(3-z)\) \(=10-3 \alpha-5+\alpha+1\) \(=6-2 \alpha\) For unique solution…
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