Question: 1. Let TR Rm be a linear transformation. (a) If T is injective, what can you determine about the relationship between m and n?

1. Let TR" Rm be a linear transformation. (a) If T is

1. Let TR" Rm be a linear transformation. (a) If T is injective, what can you determine about the relationship between m and n? If T is surjective, what can you determine about the relationship between m and n? Make sure to briefly explain your answers. (b) Let L R R be another linear transformation. Prove that the composition LoT: R" R, defined by (LoT)() L(T()), is a linear transformation. Clearly indicate where you use linearity of Land T. =

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