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Professor Dave again, lets talk image and kernel. Now that we have learned about linear transformations, we have to discuss two related concepts, and these are called image and kernel. These are best defined by example, so lets take a look at one now. Say we have a linear transformation that maps from the vector space V to the vector space W. As we know, this will involve taking vectors from V and turning them into vectors in W. If we transform a group of vectors from V, we end up starting to map out several vectors in W. This is the idea behind what we mean by image. If we take a subspace of V, lets call it S, this is a group of vectors from V that can then be transformed. The set of vectors that we can get from this transformation is what is known as the image of S. One way to think of it is that its as if we are shining a light on a part of the vector space V and seeing how much of W gets lit up. The area of W that gets lit up is our image. The image of the entire vector space V