 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/3/b/i/solution

Take the nonzero vector

1 = (1, \dots, 1)^{T}

. Its

i

th image entry under matrix multiplication is the sum of row

i

(A 1)_{i} = \sum_{j = 1}^{n} A_{ij} = λ .

Thus

A 1 = λ 1

, exhibiting

1

λ

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