 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/6/i/solution

k - 6

, so for

k \neq = 6

A^{- 1} = \frac{1}{k - 6} k - 2 - 4 k - 3 112 00 k - 6 .

The specified equations use

k = 4

, with right-hand side

(2, 3, 1)^{T}

. Multiplying by

A^{- 1} ∣_{k = 4}

gives

(x, y, z) = (\frac{1}{2}, \frac{1}{2}, - 1) .

In particular the parameter in the inverse formula must be set to four, not left arbitrary for this numerical system.

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