3 Recall the following definitions (that you should have seen in first-year) concerning transformations. A transformation T: R" →R" is a linear transformation if 1. Vu, v € R", T(u + v) = T(u) +T(v); 2. Vv € R" and Ve € R. T(cv) = cT(v). Show the following theorem. Let A E Mmn. Then the matrix transformation T₁ : R" →R" defined, for X € R", by TA(X) = AX, is a linear transformation. [Hint: do not overthink this, this literally takes two short lines!]

Fig: 1