 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-b/8/a/i/solution

False. Take the diagonal matrix

A = diag (1, 2)

x = (1, 0)^{T}

y = (0, 1)^{T}

. Their sum

(1, 1)^{T}

is mapped to

(1, 2)^{T}

, which is not a scalar multiple of that sum. More generally,

A (x + y) = a x + c y

need not have the form

λ (x + y)

when

a \neq = c

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