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Q1:

If A = then |A50| will be

A
(1 - 1002)

B
(1 - 502)

C
(1 - 1002)

D
(1 - 502)

ANS:B -

(1 - 502)

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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