Question: Condition Numbers and Geometry: Consider the linear system of equations Ax b, where A = [23] (a) Compute the eigenvalues and eigenvectors of A.

Condition Numbers and Geometry: Consider the linear system of equations Ax b, where A = [23] (a) Compute the eigenvalues and eigenvectors of A. (b) Sketch the unit circle in R, S, its image under A, A(S), and the eigenvectors of A scaled by their corresponding eigenvalue. What is the geometric interpretation of the spectral decomposition here? (c) Compute c(A). What is its geometric interpretation? (d) Derive the mathematical equation that a point in A(S) must satisfy.

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