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  1. Consider Continuous time system y(t) = x(t) - . For the system to be linear response ax1(t) + bx2(t) should be ay1(t) + by2(t) with relation between constant 'a' and 'b' as __________ .

    2. A.
    a + b = 2
    B.
    a x b = 1
    C.
    a = b
    D.
    a + b = 1

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    Answer : Option D

    Explanation :

    Let ax1(t) + bx2(t) = m(t)

    where m(t) is new input which causes the output n(t)

    n(t) = m(t) -

    n(t) = {ax1(t) + bx2(t)} -

    add and subtract

    n(t) = x1(t) -a + x2(t) -b +a +b -

    n(t) = +{a + b - 1}

    n(t) = ay1(t) + by2(t) +{a + b - 1}

    For linearity, n(t) = ay1(t) + by2(t)

    ∴ {a + b - 1} = 0 ∴ a + b = 1.

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