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  1. If A = then |A50| will be

    2. A.
    (1 - 1002)
    B.
    (1 - 502)
    C.
    (1 - 1002)
    D.
    (1 - 502)

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    Answer : Option B

    Explanation :

    An = ?

    Every n x n matrix satisfy its characteristic equation |A - λI| = 0 λ -> eigen vector

    A - λI =

    |A - λI| = = 0

    ∴ 1 =,

    ∴ f(A) = An = β0I + β1A

    Replace A by 1, I by 1

    f(λ) = λn = β0 + β1λ

    Differentiate w.r.t. λ nλn - 1 = β1

    β1 =

    ∴ β0 = λn - β x λ

    β1 =

    β0 = - = [1 - n]

    ∴ An = [1 - n]+ . 2n

    ∴ An =

    =

    ∴ A50 =

    |A50| = (1 - 502).

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