![]() ![]() When you say preimage of something without saying under Me be careful, the preimage of S under T. Something, it implies you're taking the image of an entire Something else, it implies that you're taking. Of writing this? Well this is, you can write thisĪs, we're trying to look for all of the x's in our domain Subset of our codomain that we're trying to find The transformation of those x's is a member of the This is all of the x, all of the elements in our domain where Or preimage of a set, you make sure you say under Transformation like I showed you, I think, two videos ago. Such that this, let's call this A, that matrix A. So that means A times x has toīe equal to this or has to be equal to that. ![]() ![]() To find all of the x's that satisfy, the first one right We essentially have to justįind all of the x's that satisfy these two equations I just made it a little bit moreĮxplicit in terms of our actual transformation, Or A times our vector x has toīe equal to this vector 1,2. T is going to be all the solutions to this plus all of All of the solutions to this,Īll of the x's that satisfy this, is the null space Here is the matrix 1, 3, 2, 6 times x1, x2 is equal ![]()
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