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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Determinants

NDA 2017 · Mathematics · Determinants

The equations aligned & x+2 y+3 z=1 & 2 x+y+3 z=2 & 5 x+5 y+9 z=4...

The equations x+2y+3z=12x+y+3z=25x+5y+9z=4\begin{aligned} & x+2 y+3 z=1 \\ & 2 x+y+3 z=2 \\ & 5 x+5 y+9 z=4\end{aligned}

Options

  1. Ahave the unique solution
  2. Bhave infinitely many solutions
  3. Care inconsistent
  4. DNone of the above

Correct answer

A. have the unique solution

Step-by-step solution

x+2y+3z=12x+y+3z=25x+5y+9z=4\begin{aligned} & x+2 y+3 z=1 \\ & 2 x+y+3 z=2 \\ & 5 x+5 y+9 z=4 \end{aligned} Writing in matrix form, Ax=B\mathrm{Ax}=\mathrm{B}A=[123213559]∣A∣=1(9−15)−2(18−15)+3(10−5)=−6−2(3)+3(5)=−12+15=3≠0\begin{aligned} & A=\left[\begin{array}{lll} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 5 & 5 & 9 \end{array}\right] \\ & |A|=1(9-15)-2(18-15)+3(10-5) \\ & =-6-2(3)+3(5)=-12+15=3 \neq 0 \end{aligned}$ So, these equations have unique solution
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