 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/14/b/solution

A homogeneous square linear system has a nonzero solution exactly when its coefficient matrix is singular. Here

det 111 12 - 3 10 λ = λ - 5.

Thus

λ = 5.

For this value, the second equation gives

x = - 2 y

and the first gives

z = y

; the third then holds automatically. All solutions are

t (- 2, 1, 1)

, with

t \neq = 0

for the nonzero ones.

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