 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/12/b/ii/solution

a = 2

, eliminate the first column by

R_{2} \leftarrow R_{2} - 2 R_{1}

and

R_{3} \leftarrow R_{3} - 2 R_{1}

in the augmented matrix. The last two rows give

- z = - 2

and

- y + z = - 1

. Hence

z = 2

y = 3

, and the first row then gives

x = - 2

. Thus

(x, y, z) = (- 2, 3, 2) .

The coefficient determinant at this parameter is nonzero, so this solution is unique.

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