Question: for the following maps, determine whether they are linear transformations or not...totally confused help!

For the following maps, determine whether they are linear transformations or not, and present an
appropriate proof.


(a) T : R^4 → M2,3 given by T(a, b, c, d) =  [a   a^2   a^3
                                                                   b    c       d ]
.
(b) T : M2,3 → M3,2 given by T(M) = M^T (transpose of M)
.
(c) T : P3 → P3 given by T(p(x)) = p(2) + 3x · p'(x), where p'(x) denotes the derivative of the polynomial p(x).

 

i know that the 2 rules for proving are T (u+v)= T(u) + T (v) and T (ku)= k T (u).....but how do i show it with the questions above, like do i just take any numbers , so confused

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