Multiple Choice Questions on If a b c are non zero real numbers then the inverse of the matrix ........ for NDA Exam Preparation

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Multiple Choice Questions

If a b c are non zero real numbers then the inverse of the matrix ........

Mathematics (NDA) Matrices and Determinants
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    If a, b, c are non-zero real numbers, then the inverse of the matrix

    \begin{bmatrix} a & 0 & 0\\ 0 & b & 0 \\ 0 &0 & c \end{bmatrix} is\: equal\: to

    \begin{bmatrix} a^{-1} & 0 & 0\\ 0 & b^{-1} & 0 \\ 0 &0 & c^{-1} \end{bmatrix}

    Incorrect Answer

    \frac{1}{abc}\begin{bmatrix} a^{-1} & 0 & 0\\ 0 & b^{-1} & 0 \\ 0 &0 & c^{-1} \end{bmatrix}

    Correct Answer

    \frac{1}{abc}\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 &0 & 1 \end{bmatrix}

    Incorrect Answer

    \frac{1}{abc}\begin{bmatrix} a & 0 & 0\\ 0 & b & 0 \\ 0 &0 & c \end{bmatrix}

    Incorrect Answer
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    Explanation:

    \begin{bmatrix} a & 0 & 0\\ 0 & b & 0 \\ 0 &0 & c \end{bmatrix} a=diag[a,b,c]
    A^{-1}=diag^{-1}[a,b,c]=\frac{1}{| A| }diag^{-1}[a^{-1},b^{-1},c^{-1}]
    =\frac{1}{abc}\begin{bmatrix} a^{-1} & 0 & 0\\ 0 & b^{-1} & 0 \\ 0 &0 & c^{-1} \end{bmatrix}
     

    By: Munesh Kumari
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