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**[SOLVED] linear algebra determinant of linear operator**

**1. Homework Statement**

Let T be a linear operator on a finite-dimensional vector space V.

Define the determinant of T as: det(T)=det([T]β) where β is any ordered basis for V.

Prove that for any scalar λ and any ordered basis β for V that det(T - λIv) = det([T]β - λI).

**2. Homework Equations**

Another part of the problem yielded that for any two ordered bases of V, β and γ , that det([T]β) = det([T]γ).

**3. The Attempt at a Solution**

I need someone to help me understand the notation. I don't actually know what I am being asked to prove here.