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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    The value of determinant \[\left| \begin{matrix}    {{\sin }^{2}}13{}^\circ  & {{\sin }^{2}}77{}^\circ  & \tan 135{}^\circ   \\    {{\sin }^{2}}77{}^\circ  & \tan 135{}^\circ  & {{\sin }^{2}}13{}^\circ   \\    \tan 135{}^\circ  & {{\sin }^{2}}13{}^\circ  & {{\sin }^{2}}77{}^\circ   \\ \end{matrix} \right|\]is

    A) \[-1\]

    B) \[0\]

    C) \[1\]

    D) \[2\]

    Correct Answer: B

    Solution :

    [b] \[\left| \begin{matrix}    {{\sin }^{2}}13{}^\circ  & {{\cos }^{2}}13{}^\circ  & -1  \\    {{\cos }^{2}}13{}^\circ  & -1 & {{\sin }^{2}}13{}^\circ   \\    -1 & {{\sin }^{2}}13{}^\circ  & {{\cos }^{2}}13{}^\circ   \\ \end{matrix} \right|\] \[=\left| \begin{matrix}    0 & {{\cos }^{2}}13{}^\circ  & -1  \\    0 & -1 & {{\sin }^{2}}13{}^\circ   \\    0 & {{\sin }^{2}}13{}^\circ  & {{\cos }^{2}}13{}^\circ   \\ \end{matrix} \right|=0\] Applying \[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}}\]


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