3. (a) Use change-of-basis techniques to construct a 2 x 2 matrix A that satisfies the following eigenvector equations: A 3 4 (²)=³(²), A(-¹2) = 5 (-²2). Please write your matrix A relative to the standard basis. (b) Now suppose that {v₁, v2} is a basis for R2 and that A₁, A2 are scalars. Describe a general formula to construct a 2 x 2 matrix B such that Bu; = Aivi for i=1, 2, where B is written with respect to the standard basis. How many possible matrices B are there that satisfy these equations?

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