Diagonalization of Symmetric Matrices Example 1: Consider the matrix. -5] A = 3 -5 3 a) Find the eigenvalues A₁, A₂ of A and find a basis for each eigenspace. = b) Find an orthonormal basis {u₁, u2} for R2 of eigenvectors of A (where Au₁ Au₂ = X₂U₂). A₁u₁ and c) Is A diagonalizable? If A is diagonalizable, find matrices P and D such that A = PDP-¹ d) Plot the eigenspaces of A using the bases found in part a). X2 4 2 X1 -4 2 -2 -4 2
