JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For the system of linear equations \(2 x+4 y+2 a z=b\) \(x+2 y+3 z=4\) \(2 x-5 y+2 z=8\) which of the following is NOT correct?
- A It has infinitely many solutions if \(a=3, b=6\)
- B It has unique solution if \(a=b=6\)
- C It has unique solution if \(a=b=8\)
- D It has infinitely many solution if \(a=3, b=8\)
Answer & Solution
Correct Answer
(A) It has infinitely many solutions if \(a=3, b=6\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}2 & 4 & 2 a \\ 1 & 2 & 3 \\ 2 & -5 & 2\end{array}\right|=18(3-a)\) \(\Delta_x=\left|\begin{array}{ccc}b & 4 & 2 a \\ 4 & 2 & 3 \\ 8 & -5 & 2\end{array}\right|=(64+19 b-72 a)\) For unique solution \(\Delta=0\) \(\Rightarrow a \neq 3\) and…
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