JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The following system of linear equations \(2 x+3 y+2 z=9\) ; \(3 x+2 y+2 z=9\) ;\(x-y+4 z=8\)
- A has a solution \((\alpha, \beta, \gamma)\) satisfying \(\alpha+\beta^{2}+\gamma^{3}=12\)
- B has infinitely many solutions
- C does not have any solution
- D has a unique solution
Answer & Solution
Correct Answer
(D) has a unique solution
Step-by-step Solution
Detailed explanation
\(2 x+3 y+2 z=9....(1)\) \(3 x+2 y+2 z=9....(2)\) \(x-y+4 z=8....(3)\) \((1)-(2) \Rightarrow-x+y=0 \Rightarrow x-y=0\) from \((3) 4 z=8 \Rightarrow z=2\) from \((1)\) \(2 x+3 y=5\) \(\Rightarrow x=y=1\) \(\therefore\) system has unique solution
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