Define linear transformation. Show that the mapping T:V₂ (R)→V₂ (R) defined as Tq,a,a)=(3-2a +a, q-3a-2a) is a linear transformation from V₂ (R) into V₂(R).
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A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map. ... The two vector spaces must have the same underlying field.
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