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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Determinants

NDA 2023 · Mathematics · Determinants

The system of linear equations x+2 y+z=4,2 x+4 y+2 z=8 and 3 x+6...

The system of linear equations x+2y+z=4,2x+4y+2z=8x+2 y+z=4,2 x+4 y+2 z=8 and 3x+6y+3z=103 x+6 y+3 z=10 has

Options

  1. Aa unique solution
  2. Binfinite many solutions
  3. Cno solution
  4. Dexactly three solutions

Correct answer

B. infinite many solutions

Step-by-step solution

x+2 y+z=42 x+4 y+2 z=83 x+6 y+3 z=10D=\left|121242363\begin{array}{lll}1 & 2 & 1 \\ 2 & 4 & 2 \\ 3 & 6 & 3\end{array}\right|=0D_1=\left|4218421063\begin{array}{ccc}4 & 2 & 1 \\ 8 & 4 & 2 \\ 10 & 6 & 3\end{array}\right|=0D_2=\left|1412823103\begin{array}{ccc}1 & 4 & 1 \\ 2 & 8 & 2 \\ 3 & 10 & 3\end{array}\right|=0D_3=\left|1242483610\begin{array}{ccc}1 & 2 & 4 \\ 2 & 4 & 8 \\ 3 & 6 & 10\end{array}\right|=0\because D=D_1=D_2=D_3=0\therefore \quad System has infinite solutions.
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