Given T(x2x1)=(sinx2cosx1)Let α be a scalar and (y2y1) be vector then: T((x2x1)+α(y2y1))=T(x2+αy2x1+αy1)=(sin(x2+αy2)cos(x1+αy1))=(sinx1cosαy1+cosx1sinαy1cosx1cosαy1−sinx1sinαy1)And T(x2x1)+αT(y2y1)=(sinx2cosx1)+α(siny2cosy1)=(sinx2+αsiny2cosx1+αcosy1)=(sinx1cosαy1+cosx1sinαy1cosx1cosαy1−sinx1sinαy1)=T((x2x1)+α(y2y1))⟹T(x2x1)+αT(y2y1)=T((x2x1)+α(y2y1))∴The given transformation is not a linear transformation.
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