Question: Please solve on paper and should be clear everything thanks! Given -5 2 3 7 Q = 210 3 O -1 a) (10) Find a

Please solve on paper and should be clear everything thanks!

Given -5 2 3 7 Q = 210 3 O -1 a) (10) Find a non-singular matrix P such that P-'Q P = D is diagonal. Find D. b) (7) Find the spectral decomposition of Q c) (8) Identify a quadratic form associated with this matrix. Make an orthogonal rotation that eliminate the cross terms in this quadratic form Q. Express Q in terms of new variables x, y, z. Identify and specify the new surface on the new axis system for Q = 28

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