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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Determinants

NDA 2020 · Mathematics · Determinants

For how many values of k , is the matrix [ array ccc 0 & k & 4 -k &...

For how many values of kk, is the matrix \left[0k4−k0−5−kk−1\begin{array}{ccc}0 & k & 4 \\ -k & 0 & -5 \\ -k & k & -1\end{array}$\right] singular?$

Options

  1. AOnly one
  2. BOnly two
  3. COnly four
  4. DInfinite

Correct answer

D. Infinite

Step-by-step solution

For singular matrix, \left[0K4−K0−5−KK−1\begin{array}{ccc} 0 & K & 4 \\ -K & 0 & -5 \\ -K & K & -1 \end{array}\right]=0\begin{aligned} & K(5 K-K)+4 \left(-K^2\right)=0 \\ & 4 K^2-4 K^2=0 \end{aligned}$$Hence,forallvaluesofHence, for all values ofK,thegivenmatrixissingularmatrix., the given matrix is singular matrix.
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