PrepRung
Sign inSign up free

NDA 2023 Maths · Mathematics · Determinants · medium

The values of x for which beginvmatrixx&1&1\\1&x&1\\1&1&xendvmatrix=0 are

Single correct option

The values of xx for which ∣x111x111x∣=0\begin{vmatrix}x&1&1\\1&x&1\\1&1&x\end{vmatrix}=0 are
  1. A. 1,−21,-2
  2. B. 1,21,2
  3. C. −1,2-1,2
  4. D. −1,−2-1,-2
Show answer and solution

Answer: (A) 1,−21,-2

Adding all rows to the first gives the factor (x+2)(x+2), and the determinant is x3−3x+2=(x−1)2(x+2)x^3-3x+2=(x-1)^2(x+2). Hence x=1x=1 (repeated) or x=−2x=-2. Choosing x=−1x=-1 confuses the factor x+2x+2 with x+1x+1.
Report a mistake

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake