Answer Happy

1a. Composition of Transformations and Matrix Products Explain the following briefly using a few sentences. 1. How do we compute the sum of two linear mappings L₁ and L₂ using matrices? 2. How do we compute the composition of two linear mappings L₁ and L2 using matrices? 1b. Function Basics Given an example of a function which is 1. Injective but not surjective, 2. Surjective but not injective. Justify your answers. 2. In your own words For the following question, I want you to use your own words. A sign that you truly understand a concept is that you're able to explain it to someone else (in this case, your grader). It may take a few tries and will require some practice, so don't worry about explaining things perfectly the first time around. You will likely have to write several drafts before you come up with wording that feels right for you. The most difficult part can be getting started. I recommend that you start by writing an initial attempt (regardless of how good or bad you think it is) and iterating from there! Suppose that we have some basis B = {b₁,b2, b3} of R³. Use mathematical language (try to use as many mathematical equations as you can) to explain why knowing how a linear mapping L: R³ → R4 acts on B is enough to know how the mapping acts on all of R³.