 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2021-resit/8/c/i/solution

Write the ordered basis as

B = (1, t, e^{t}, t e^{t})

F (1) = 0, F (t) = 1, F (e^{t}) = e^{t}, F (t e^{t}) = e^{t} + t e^{t} .

The corresponding coordinate vectors form the columns of the representing matrix:

[F]_{B} = M = 0000100000100011 .

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