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## Main Question or Discussion Point

This book says that if [itex]W^aX_a=0[/itex] and [itex]X_a[/itex] is arbitrary, then I should be able to prove that [itex]W^a=0[/itex]. I don't see how this is possible. This is the equivalent of the vector dot product, so if, say, [itex]X_a=(1,0,0,0)[/itex], then [itex]W^a[/itex] could be (0,1,1,1), and the dot product would be [itex]1*0+0*1+0*1+0*1=0[/itex]. Why would [itex]W^a[/itex] have to be 0?