Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 11 / a / i / Solution

Use Gaussian elimination on the augmented matrix. First take $R_2\leftarrow R_2-R_1$ and $R_3\leftarrow R_3-2R_1$, then $R_3\leftarrow 4R_3-3R_2$:By back substitution, the last row gives $z=3$, the second gives $-4y-6=-14$ and hence $y=2$, and the first gives $x+4+9=14$. ThusThe right-hand side has been transformed in every row operation, preserving the solution set.