(b) Check whether the distributions D, and D2 are integrable: (i) D, on R is spanned...

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(b) Check whether the distributions D, and D2 are integrable: (i) D, on R is spanned by the following vector fields Z = W = %3D sf(D D2 on the special linear group S2(R) = {A€ M2x2: det(A) = 1} : R'→ R' is %3D generated by -(: :). v - ( ) cos 0 sin 0 U= %3D - sin 0 cos 0 (b) Check whether the distributions D, and D2 are integrable: (i) D, on R is spanned by the following vector fields Z = W = %3D sf(D D2 on the special linear group S2(R) = {A€ M2x2: det(A) = 1} : R'→ R' is %3D generated by -(: :). v - ( ) cos 0 sin 0 U= %3D - sin 0 cos 0