JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    Matrix \[A=\left[ \begin{matrix}    1 & 0 & -k  \\    2 & 1 & 3  \\    k & 0 & 1  \\ \end{matrix} \right]\]is invertible for  [UPSEAT 2002]

    A) \[k=1\]

    B) \[k=-1\]

    C) \[k=0\]

    D) All real k

    Correct Answer: D

    Solution :

    \[\because \] On expansion, |A| = \[{{k}^{2}}+1\], which can be never zero. Hence matrix A is invertible for all real k.


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