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f is a transformation of the plane so that f(x,y)=(a⋅x+b⋅y,c⋅x+d⋅y) for some symmetric matrix M=[[a,b],[c,d]]. It...

f is a transformation of the plane so that f(x,y)=(a⋅x+b⋅y,c⋅x+d⋅y) for some symmetric matrix M=[[a,b],[c,d]]. It is known that f(1,1)=(10,0) and f(8,1)=(52,28). Find the matrix M.

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