JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The values of \(\mathrm{m}, \mathrm{n}\), for which the system of equations \( x+y+z=4 \) \( 2 x+5 y+5 z=17 \) \( x+2 y+m z=n\) has infinitely many solutions, satisfy the equation :
- A \(m^2+n^2-m-n=46\)
- B \(m^2+n^2+m+n=64\)
- C \(\mathrm{m}^2+\mathrm{n}^2+\mathrm{mn}=68\)
- D \(m^2+n^2-m n=39\)
Answer & Solution
Correct Answer
(D) \(m^2+n^2-m n=39\)
Step-by-step Solution
Detailed explanation
\(\mathrm{D}=\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & 5 & 5 \\ 1 & 2 & \mathrm{~m}\end{array}\right|=0 \Rightarrow \mathrm{m}=2\) \(\mathrm{D}_3=\left|\begin{array}{ccc}1 & 1 & 4 \\ 2 & 5 & 17 \\ 1 & 2 & \mathrm{n}\end{array}\right|=0 \Rightarrow \mathrm{n}=7\)
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