 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014-resit/6/i/solution

A^{k} = A

for every integer

k \geq 1

. Thus any scalar polynomial reduces to

p (A) = p (0) I + [p (1) - p (0)] A,

or equivalently

a I + b A

. This expression describes all polynomials in

A

, although its two coefficients need not be unique if

A = 0

A = I

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