3 recall the following definitions that you should have seen in first
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!]
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