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 map

Ti(p) ( t) = p(t + a).

(b) Let a E F Let T2 : Fit]ten – F be the map defined by

T2 (p) = p(a).

(c) Let P be an invertible n x n matrix. Let T3 : Foxn -gt; Fn x n be the map

T3( A) = PAP-1.

(d) Let v = (v1, V2, 13) E F’ be a non-zero vector. Let TA : F3 – F be the linear map

defined by

TA((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).Math