 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/10/a/solution

All three linear equations are multiples of the first, leaving the single constraint

x + y + z = 0

. Choose two real numbers

s, t

freely:

(x, y, z) = (s, t, - s - t), s, t \in R .

A basis for this two-dimensional linear subspace is

(1, 0, - 1)^{T}, (0, 1, - 1)^{T}

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