Problem 1. (1) Orthogonally diagonalize the matrix A= (? 2 1 1 1 2 1 1 1 2 (2) Write down an expression for the quadrati

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Problem 1 1 Orthogonally Diagonalize The Matrix A 2 1 1 1 2 1 1 1 2 2 Write Down An Expression For The Quadrati 1 (336.89 KiB) Viewed 30 times

Problem 1. (1) Orthogonally diagonalize the matrix A= (? 2 1 1 1 2 1 1 1 2 (2) Write down an expression for the quadratic form q(X1, X2, x3) = xAx as a function of X1, X2, X3 E R. (3) Determine the type of the quadratic form q. Justify your arguments. (4) Find an orthogonal matrix Q such that the coordinates change y = Qx transforms the quadratic form q into a sum of squares ay,2 + by22 +cy,