Show that this decision rule is equivalent to the condition

Question

The signal vectors s₁ and s₂ are used to represent binary symbols 1 and 0, respectively, in a binary FSK system using coherent detection. The receiver decides in favor of symbol when

where xTsi is the inner product of the observation vector x and the signal vector si , i = 1, 2.

Show that this decision rule is equivalent to the condition x₁ > x₂, where x₁ and x₂ are the two elements of the observation vector x. Assume that the signal vectors s₁ and s₂ have equal energy.