4. Let B = {õ1, 2, üz} and D = {w1, w2} be bases for the real vector spaces V and W respectively. Let T :V → W be the linear transformation satisfying: T(51) = 201 – w2, T(52) = w1 – w2, and T(53)=w1+202. %3D Determine the dimensions of Ker(T) and R(T). Find bases for these subspaces. Hint: Use a matrix representation.

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A: Here we can use the composition of function formula to find the required values.

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