Question: (c) Let S : R4 - R be a linear transformation whose kernel, ker(S) C R*, is described by the system of Cartesian equations 21

(c) Let S : R4 - R be a linear transformation whose kernel, ker(S) C R*, is described by the system of Cartesian equations 21 - 3x3 = 0 and 12 - 414 = 0. Moreover, let 7' : IR3 -> R* be a linear transformation and consider the composition (SOT) : R3 - R3 defined by (S . T) (x) := S(T(x)). (i) Express ker(S) as the linear span of a suitable set of vectors in IR4. (ii) Letting T be represented by a matrix A, that is, letting T(x) = Ax for all x ( R3, find an A such that ker (T) = Lin and ker (S . T) = R3

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