 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/13/b/i/solution

A r = d

with

A = 131243354, r = x y z, d = 123 .

Expansion along the first row gives

det A = (16 - 15) - 2 (12 - 5) + 3 (9 - 4) = 2

. Since $det A = 2 \neq = 0$ ,

A

r = A^{- 1} d

is the unique solution for this right side.

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