 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/18/c/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

det 210131 0 μ 2 = 2 (6 - μ) - 2 = 10 - 2 μ .

A homogeneous linear system has a nonzero solution exactly when this is a singular matrix. Therefore

μ = 5.

At this value all solutions are

(x, y, z) = t (1, - 2, 1)

, with

t \neq = 0

for a nonzero solution.

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