Posted: December 30th, 2021

3. Determine whether the following linear maps are invertible. If they are, give an inverse.If not, then explain why it is not invertible.(a) Let a E F. Define T1 : F[ten – F[ten by the mapTi(p) ( t) = p(t + a).(b) Let a E F Let T2 : Fit]ten – F be the map defined byT2 (p) = p(a).(c) Let P be an invertible n x n matrix. Let T3 : Foxn -> Fn x n be the mapT3( A) = PAP-1.(d) Let v = (v1, V2, 13) E F’ be a non-zero vector. Let TA : F3 – F be the linear mapdefined byTA((21, 2, 23) ) = V121+ 02×2 + 032’3(e) Let 75 : F4 – F be the linear map defined by Ts ((x1, X2, X3, 24) ) = (23, X2, 24, 21).

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