Past exam of the mathematical methods I course of the University of Oxford / 2019 / 12 / a

The linear system has the matrix formThe first equation gives $3x_2+2x_3=-4$. Substitute it into the second to obtain $x_1=2+4x_2+2x_3=x_2-2$. Substitution into the third gives $x_2+x_3=-7$. ConsequentlyIt follows thatSubstitution verifies all three equations. Also $\det A=1\ne 0$, so this solution of a linear system is unique.