Multiple Choice Questions on For a matrix C if CT C 1 Find the value of x ........ for NDA Exam Preparation

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Multiple Choice Questions

For a matrix C if CT C 1 Find the value of x ........

Mathematics (NDA) Matrices and Determinants
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    For a matrix C=\begin{bmatrix} 3/5 & 4/5\\ x & 3/5 \end{bmatrix}  if CT   =C-1  Find the value of x?

    4/5

    Incorrect Answer

    -4/5

    Correct Answer

    -5/4

    Incorrect Answer

    3/5

    Incorrect Answer
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    Explanation:

    Given  CT   =C-1   then C is orthogonal (according to orthogonal matrix properties)

    A A-1  =I    (using properties)

    CT C=C CT  =I

    \begin{bmatrix} 3/5& x\\ 4/5 & 3/5 \end{bmatrix}\begin{bmatrix} 3/5 & 4/5\\ x & 3/5 \end{bmatrix} =\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}?

    \begin{bmatrix} 9/25 + x^{2} &12/25 +3/5x \\ 12/25 +3x/5 & 16/25 +9/25 \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}

     

    12/25  +3x/5   =0

    3x/5   =-12/25

    X=-4/5

     

    By: bhavesh kumar singh
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