Prove results similar to Exercises 46 and 47 for the adjoint of a linear operator on a real or…

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Prove results similar to Exercises 46 and 47 for the adjoint of a linear operator on a real or complex inner product space.

Exercise 46 & 47

46. Let T : V → W be a linear map. (a) Prove ker(T ) = A(img(T)). (b) Deduce that T is injective iff T is surjective.

47. Let T : V → W be a linear map. (a) Prove img(T ) = A(ker(T)). (b) Deduce that T is surjective iff T is injective

 

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