# Let V be a finite-dimensional vector space with ordered bases α, β, and γ.(a) Prove that if Q and R are the change of coordinate matrices that change α-coordinates into β-coordinates and β-coordinates into γ-coordinates, respectively, then RQ is the change of coordinate matrix that changes α-coordinates into γ-coordinates. (b) Prove that if Q changes α-coordinates into β-coordinates, then Q−1 changes β-coordinates into α-coordinates.

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Let V be a finite-dimensional vector space with ordered bases α, β, and γ.(a) Prove that if Q and R are the change of coordinate matrices that change α-coordinates into β-coordinates and β-coordinates into γ-coordinates, respectively, then RQ is the change of coordinate matrix that changes α-coordinates into γ-coordinates. (b) Prove that if Q changes α-coordinates into β-coordinates, then Q−1 changes β-coordinates into α-coordinates.

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Step 1

Let V be a finite-dimensional vector space with ordered bases α, β, and γ

Step 2

Now, find the matrix RQ ...

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### Applications of Mathematics 