JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The following system of linear equations \(7 x+6 y-2 z=0\) ; \(3 x+4 y+2 z=0\) ; \({x}-2{y}-6{z}=0,\) has
- A infinitely many solutions, \((\mathrm{x}, \mathrm{y}, \mathrm{z})\) satisfying \(x=2 z\)
- B no solution
- C only the trivial solution
- D infinitely many solutions, \((\mathrm{x}, \mathrm{y}, \mathrm{z})\) satisfying \(y=2 z\)
Answer & Solution
Correct Answer
(A) infinitely many solutions, \((\mathrm{x}, \mathrm{y}, \mathrm{z})\) satisfying \(x=2 z\)
Step-by-step Solution
Detailed explanation
\(7 \mathrm{x}+6 \mathrm{y}-2 \mathrm{z}=0\dots(1)\) \(3 x+4 y+2 z=0\dots(2)\) \(\mathrm{x}-2 \mathrm{y}-6 \mathrm{z}=0\dots(3)\) \(\Delta=\left|\begin{array}{ccc}{7} & {6} & {-2} \\ {3} & {4} & {2} \\ {1} & {-2} & {-6}\end{array}\right|=0 \Rightarrow\) infinite solutions Now…
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