Chapter 3 - Determinants - 3.2 Determinants and Elementary Operations - 3.2 Exercises - Page 118: 21

$$\left|\begin{array}{rrr}{1} & {0} & {2} \\ {-1} & {1} & {4} \\ {2} & {0} & {3}\end{array}\right|=-1.$$

\begin{align*} \left|\begin{array}{rrr}{1} & {0} & {2} \\ {-1} & {1} & {4} \\ {2} & {0} & {3}\end{array}\right|&=\left|\begin{array}{rrr} {1} & {4} \\ {0} & {3}\end{array}\right|-0 \left|\begin{array}{rrr} {-1} & {2} \\ {4} & {3}\end{array}\right|+2\left|\begin{array}{rrr} {-1} & {1} \\ {2} & {0}\end{array}\right|\\ &=3+2(-2)\\ &=-1. \end{align*}