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

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

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