MATH118 Injective and Surjective Linear Transformations

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10:57 I didnt get it. In the case that d = 0, it has infinite solutions, and by that, T is injective (why?), but what if d is not 0?
Plus, if KerT is non trivial, wouldnt it be sufficient to say it is injective?
By the way, thanks for the video

Gabriel-oytp