Question

Construct a linear transformation T : R4 → R4 such that Kernel(T) = Image(T). How about the same for a linear transformation S : R5 →R5.

Answer 1

Answer:

Take T:(a,b,c,d)↦(c,d,0,0) for R4,

but for R5 there is none,

because dim(Ker)+dim(Im)=dim(space),

so if dim(Ker)=dim(Im) then dim(space) is even.

Step-by-step explanation:

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