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JEE Main 2010
Exam
JEE Main
Year
2010
Subject
Mathematics
Chapter
Determinants

JEE Main 2010 · Mathematics · Determinants

Consider the system of linear equations: aligned & x_1+2 x_2+x_3=3...

Consider the system of linear equations: x1+2x2+x3=32x1+3x2+x3=33x1+5x2+2x3=1\begin{aligned} & x_1+2 x_2+x_3=3 \\ & 2 x_1+3 x_2+x_3=3 \\ & 3 x_1+5 x_2+2 x_3=1 \end{aligned} The system has

Options

  1. Aexactly 3 solutions
  2. Ba unique solution
  3. Cno solution
  4. Dinfinite number of solutions

Correct answer

C. no solution

Step-by-step solution

D=∣121231352∣=0D1=∣321331152∣≠0\begin{aligned}& D=\left|\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 5 & 2 \end{array}\right|=0 \\ & D_1=\left|\begin{array}{lll}3 & 2 & 1 \\ 3 & 3 & 1 \\ 1 & 5 & 2 \end{array}\right| ≠ 0 \end{aligned}\Rightarrow Given system, does not have any solution. \Rightarrow No solution.
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