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Linear Transformations Worksheet

Linear Transformations Worksheet

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You now know what a transformation is, so let's introduce a special kind of transformation called a linear transformation. It only makes sense that we have something called a linear transformation because we're studying linear algebra. We already had linear combinations so we might as well have a linear transformation. And a linear transformation, by definition, is a transformation-- which we know is just a function. We could say it's from the set rn to rm -- It might be obvious in the next video why I'm being a little bit particular about that, although they are just arbitrary letters -- where the following two things have to be true. So something is a linear transformation if and only if the following thing is true. Let's say that we have two vectors. Say vector a and let's say vector b, are both members of rn. So they're both in our domain. So then this is a linear transformation if and only if I take the transformation of the sum of our two vectors. If I add them up first, that's e

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