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7. Consider the symmetric matrix A = [ 4 5 5 6 ] . (a) Find an invertible matrix M and a diagonal matrix D
7. Consider the symmetric matrix A = [4556] .
(a) Find an invertible matrix M and a diagonal matrix D such that MT AM = D.
(b) Consider the quadratic form Q(x) = xT Ax where x = [x1x2] R2.
Find an invertible matrix P such that y = Px and the quadratic form has no cross
terms, i.e., Q(y) = Q(y1,y2) = ay12 + by22 for some a,b R.
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