 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-i/2/c/iii/solution

x_{3}

is possible precisely when

λ = 5

and

μ = 2

. Thus

infinitely many solutions ⟺ (λ, μ) = (5, 2) .

x = 120 + t - 2 - 5 1, t \in R .

The direction vector spans the kernel, and the displayed straight line is the entire solution set of a linear system.

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