Chapter 9 - Systems and Matrices - 9.3 Determinant Solution of Linear Systems - 9.3 Exercises - Page 887: 96

$$\left\{ 0 \right\}$$

$$\eqalign{ & \left| {\matrix{ { - 0.5} & 2 \cr x & x \cr } } \right| = 0 \cr & {\rm{Expand\, the \,determinant\, to \,obtain}} \cr & \left( { - 0.5} \right)\left( x \right) - \left( 2 \right)\left( x \right) = 0 \cr & - 0.5x - 2x = 0 \cr & {\rm{Solve\, the\, equation}} \cr & - 2.5x = 0 \cr & x = 0 \cr & {\rm{The\, solution \,set \,is}} \cr & \left\{ 0 \right\} \cr} $$