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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Determinants

NDA 2017 · Mathematics · Determinants

If a ≠ b ≠ c , then one value of x which satisfies the equation |...

If a≠b≠ca \neq b \neq c, then one value of xx which satisfies the equation \left|0x−ax−bx+a0x−cx+bx+c0\begin{array}{ccc}0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0\end{array}\right|=0 is given by

Options

  1. Aa
  2. Bb
  3. Cc
  4. D0

Correct answer

D. 0

Step-by-step solution

\left|0x−ax−bx+a0x−cx+bx+c0\begin{array}{ccc} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{array}\right|=0 We know, the value of symmetric matrix's determinant is 0 \left|0−a−ba0−c bc0\begin{array}{ccc} 0 & -\mathrm{a} & -\mathrm{b} \\ \mathrm{a} & 0 & -\mathrm{c} \\ \mathrm{~b} & \mathrm{c} & 0 \end{array}\right|=0 In the given matrix, determinant is 0 , if x=0x=0
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