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NDA 2025 Maths · Mathematics · Matrices · hard

The system x+y+z=1, x+2y+3z=4, x+3y+kz=6 does NOT have a unique solution when k equals

Single correct option

The system x+y+z=1x+y+z=1, x+2y+3z=4x+2y+3z=4, x+3y+kz=6x+3y+kz=6 does NOT have a unique solution when kk equals
  1. A. 33
  2. B. −5-5
  3. C. 55
  4. D. 00
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Answer: (C) 55

A unique solution requires a non-zero coefficient determinant. ∣11112313k∣=(2k−9)−(k−3)+(3−2)=k−5\begin{vmatrix}1&1&1\\1&2&3\\1&3&k\end{vmatrix}=(2k-9)-(k-3)+(3-2)=k-5. It vanishes at k=5k=5, where the system is singular.
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