Question

let V be the space spanned by v1=cos^2x ,v2=sin^2x ,v3=cos2x
a)show that S={ v1,v2,v3} is not a basis for V
b) find a basis for V

Answer 1

a) \[\cos ^2(x)- \sin ^2(x)-\cos(2x)=0\]
b) {\(\cos^2(x),\sin^2(x)\) }